Anybody have any suggestions to increase the strength and muscle endurance of my squeeze. I need some help controlling the legs in jiu jitsu and find myself need a bit more strength and endurance to do so.
What are your stats on some core lifts? Overhead press, bench press, squat, weighted pull ups, deadlift... What weight division are you in? 
Bench press, rows/pulls. Pair them together on the same workout day push/pull format.
Honestly though if youre gonna hit the gym, might as well train your whole body; you dont want to be an upperbody only guy. Stronger legs and back improve your performance in so many ways as well(ie a strong legs and back help posturing and basing out, which is important for leg control esp. against much bigger guys- your kinetic chain is only as strong as its weakest link), and it doesnt take much weekly gym time to have an effective program.
531 is a good basic low volume program to start with if you do the the the bare bones versions without the assistance work for the 4 core lifts, and pair some horizontal/vertical pulling (bent over/dumbelll rows and pullups/pulldowns for example) on your bench press and overhead pressing days respectively, you have a solid program with minimal time investment. Experiment versions w/ more volume down the road if you feel inclined.
If you need instructional video for lifting technique on the 4 basic lifts i have some youtube recommendations.
Find a large punching bag, wrap your arms around it without locking your hands and hold yourself off the ground for time. 
I am 5'9 200-219 (depending on my diet). I have been doing 5x5 lifts for about a year. Recently, I have raised the weight and done 3x5 just to see how it will effect my numbers. I had both knees scoped last year so my legs are a bit behind the rest of me. squatting is still difficult but I am, for the most part, hitting these lifts twice a week:
bench 5x5-255 or 5x3 275
deadlift-5x5 375 or 3x5 405
overhead press-5x5 155 or 3x5 175
Squat-5x10 275 5x5 295
bent over row-5x5 185
I have also incorporated these exercises and lifts in here and there:
weighted dips-5x5 with 70 lbs...unweighted at the end of the workout=16 dips
towel pull ups 5x5
lat pull downs 5x8 170
I seem to remember seeing some drills with sandbags a few years ago which were supposed to help with guillotine type strength.
Google or YouTube maybe.
Which muscles or muscles groups am I focussing on in my squeeze. The core is obvious but what else? Lats? Pecs?
Your whole upper body, when you say "squeeze" what specific positioning are you referring to just two arm hugging? Hands clasped?
Your lats/back is important, but honestly everything in your back/chest/arms comes into play at some point.
Your numbers arent bad, perhaps its a technique issue- when you roll, are you using your weight/shifting your hips properly? Do you have a qualified instructor supervising?
Just a general squeeze to neutralize their legs. I will clasp my hands if I can get all the way around but sometimes it's just downward shoulder pressure. we have one guy who is 6'3 240 with huge legs/hips/butt. My instructor uses speed and agility to pass his guard but I can't seem to get passed his legs. I'm not small nor am I a cardio machine so I usually use a smash pass style rather than the small guy style of passing.
Instructor is great...3 time World champ...4 stripe black belt. I don't have trouble passing everyone, but big/long legged guys are more difficult.
Your opponents weigh almost as much as your lifts. Being in a lower weight class will be the surest way to strengthen your grip for competition.
If by smash pass you mean using double underhooks to clasp your hands aroudn his legs and push his legs over to the side, (the smash passes I'm thinking of dont really require substamtial squeezing strength or any squeezing at all), your biceps, shoulders and pecs will help you force your hands together to clasp. You also drive with your legs and hips while maintaining a tight "core" to help push their thighs with your shoulders. Once clasped, your lats and back will facilitate keeping a tight hold.
Buuut, if you really have to muscle it, this kind of goes against juijitsu philosophy I think?
Long legs will def make a guard harder to pass.
Have you tried knee slide methods? They aren't something I'd call small man only or speed oriented game. You also almost never see a double underhook pass at higher levels of competition.
I would ask your instructor about advice re: alternate methods you could use to pass. Or maybe even posting in the BJJ forum.
If your bad cardio is a result of being overweight, losing weight, or doing cardio might be more beneficial for your performance in bjj than more weightroom time.
Do you have an aversion to losing weight?
HERTSWENIP - If by smash pass you mean using double underhooks to clasp your hands aroudn his legs and push his legs over to the side, (the smash passes I'm thinking of dont really require substamtial squeezing strength or any squeezing at all), your biceps, shoulders and pecs will help you force your hands together to clasp. You also drive with your legs and hips while maintaining a tight "core" to help push their thighs with your shoulders. Once clasped, your lats and back will facilitate keeping a tight hold.
Buuut, if you really have to muscle it, this kind of goes against juijitsu philosophy I think?
Long legs will def make a guard harder to pass.
Have you tried knee slide methods? They aren't something I'd call small man only or speed oriented game. You also almost never see a double underhook pass at higher levels of competition.
I would ask your instructor about advice re: alternate methods you could use to pass. Or maybe even posting in the BJJ forum.
If your bad cardio is a result of being overweight, losing weight, or doing cardio might be more beneficial for your performance in bjj than more weightroom time.
Do you have an aversion to losing weight?
I have lost 20 lbs in the past 6 months just to see how it would effect my game. My cardio is better and my strength is about the same (noticed a small decrease). My problem at the lower weights is the type of game. I have a harder time with the smaller man's game. I do much better against the bigger guys. Also, some weight class go from 190-209. I do not want to drop below 190. I am on the higher end of the weight class, which is where I would want to be in any weight class.
Knee slice is difficult with these 2 particular guys. I do try double under but also the bull fighter or x pass. A lot of times I beat their legs but they sneak the top one in and I end up hugging both legs and try to smash from there.
My instructor is a 135 lbs, 3 time World champ with 30 years of jiu jitsu experience. He plays a quick game. I cannot replicate his passes to beat these guys so I'm trying to take a different approach.
Shark tank,
What belt level are you?
Brown...worked mostly on my guard game from late blue through purple. Had 2 knee injuries at purple that kept me from playing a top game. I'm finally feeling better and trying to play more top/pass game.
The two guys I am talking about are beasts. One is 6'2 240-250 and brown belt. The other is 6'1 210 purple belt who is a med heavy blue belt world champ and now making some progress in the purple belt division. He is a concrete worker, former D3 wrestler who is a superb athlete.
I'm just trying to figure out a different approach to passing because my instructor is the only guy I see passing their guards.
Hmm, maybe Watch video of stocky guys who are short for their weight class and had to regularly compete against much taller opponents; Marcelo Garcia, jeff monson or Liborio for example.
If you're a hulky guy like Kevin Randleman or jeff monson, then maintaining weight might make sense, but if you have a lot of fat mass then I think leaning out would be better; you move a lot quicker with less dead weight too. But if you're 5'9 200-220 lbs of solid muscle, you have a ton of room to improve your strength
Enter an underground fighting tournament in which all competitors fight to the death. Best believe your "squeeze" will be improved when you emerge victorious.
I don’t think you’ll find an easy answer from the S&C forum. Clearly the skill level and experience of these two opponents is the main reason why you’re having so many problems with them. And as long as these two opponents keep on developing and refining their jiujitsu skills you’ll still have problems with them even if you were to build your strength.
The reason why your instructor is able to do well against them is not just because he has a quick and agile style but, more so, because he has 30 years of experience and has likely faced bigger opponents many times in his career.
I think you’ll naturally develop a method and style to deal with these two opponent in time as you continue to practice jiujitsu.
shark tank - Which muscles or muscles groups am I focussing on in my squeeze. The core is obvious but what else? Lats? Pecs?
Biceps, IMO. But as all the others have said, technique matters far more than strength.
One more piece of advise, if you're not already doing it then strengthen your rotator cuffs. It didn't add anything to my gym lifts, but in wrestling and just playing around, i felt it made me better able to express my upper body strength more efficiently when you're struggling in awkward positions or pushing/pulling at weird angles.