As he was very premature the parents are almost inevitably going to be ultra protective and nervous and that is totally understandable. Your DIL is now also pregnant again and will be even more nervous, terrified of an early birth and the hell they went through happening all over again just as you have acknowledged.
You have told us what your son has said ...but not any reasons given by your DIL....those are the most significant for you surely as she has managed to open up to you.
That said …..
for instance, they didn't want pictures of their son on fb, which I didn't know or think to ask until I posted some (after they posted some), at which time they flipped. So I apologized for it and it didn't happen again
They should have told you the FB rule re pictures. Yes you could have asked, but the problem is that because so many GPs/Parents happily post on FB, it might not have even dawned on you. A mistake, but human!
At my GS bday, I put a post up on fb about how happy I am that he is a year old and doing well! I didn't name him, but they flipped again and said "nothing about (Name) can go on fb ever!
Again they should have made clear that it wasn't just no pictures on FB, it was no mention atall.
She says that she grew up with little affection and only kisses her husband and son. No one else and feels uncomfortably if I give the little guy a kiss on his head or cheek. My kids grew up with us tickling them, horsing around together, etc. My son does it, but, apparently, she doesn't want us to play with him on our hands and knees.
Hmmm...her comment about her childhood should explain aspects of her wider approach re her son, to you! This is hard for you if you babysit sometimes, but is her right. However, she may want to think about what she expects of babysitters!
Ever since he first came home 8 months ago, he always cries and fuzzes when his diapers get changed or he gets dressed. I barely remember it, but, apparently I made a remark something like "you'll be ok, mommy is not hurting you", and she took offence to it cause it somehow implied that she is hurting him.
Again, her comment about her childhood should tell you something about why she took this the way she did
One time they left him behind with us but without food. He was hungry and I gave him a little bit of the exact same table food she had given him the night before. Wrong thing to do. She said I should've called her first--but they were at the movie theater at the time
Their mistake, should have left food. If they want to use you as a babysitter they have to allow you to take a little initiative in the best interests of their child whilst in your care. Every last event cannot be controlled, but what food to give him can be and that is up to them so they need to get organised. . But her response, in the light of her previous comments about her childhood, should tell you something about why she reacted like this. If they leave him with you again, you could ring every time there is a decision to be made about him to ask what they would like you to do! The downside of that is it might give a reason to say they won't leave him again as you are incapable of making a decision ...so maybe you can't win! If they ask why you ring, remind of conversation re food, say you just want to do the right thing for them and for your grandson
He's allowed to play with their phones but they get mad if he grabs my phone
Ask them why that is a problem?
Re the staying, at the moment I would just leave that, they really can choose where they stay and DIL clearly and understandably wants to stay with her family at the moment. Despite her description of her childhood, her family is still clearly her preference.
I know this must be stressful and worrying for you and I certainly understand the eggshell treading! 
Two men charged with assaulting police officers after the Manchester Airport brawl
