Asking anyone to sign a contract like that, sight unseen, is really an indication that something is off in your father's head. Also, the fact that this person has a contract stating no one can sue him after the fact says that there is something shady about his dealings. Who needs a pre-emptive "You Won't Sue Me" contract? Someone that's about to swindle someone. Any clear thinking person would agree.
Since your father is acting this unreasonable and his decision could cause irrepairable harm to his financial well being, why not take the matter to court and get power of attorney over your father's financial affairs?
I do agree - is your self esteem worth your inheritence? You may think so - you're here because you want your inheritance, and it appears you don't really like your father but you do things to make it seem that you do, such as visiting him each weekend - and if you do, sign the document. Just know this - if you're being asked to sign something waiving your right to sue, this person may be able to attach more than the apartment after your father dies. By signing the document, you may be giving up more than the apartment. There's a reason your father doesn't want you reading it.
EDIT: Who is right? Between you and your husband? You aren't on opposing sides really. You both are only interested in your inheritance. Not once have you mentioned your father possibly being ripped off. Your husband goes as far as saying 'do whatever you need to do but get that money!'.
So hubby says suck up to the old bastard in hopes of getting to read the document. You say it won't do any good. All your husband said was give it a try. If it doesn't work, what harm has happened? How is your position different than it is now?
Maybe your father knows all you're interested in is your inheritance and you and your sis can't wait for him to finally kick off so you can get 'what's yours'. Maybe he doesn't care what's in that contract since he knows you're only interested in your financial gain and not his. He's trying to set up a reverse mortgage so he will have money to live on. He's not interested in what happens after he dies, and if he's a narcissist he can probably tell you're in it for the money. Regardless of this 'anti-sue' contract, if he takes a reverse mortgage, the property is gone. He's basically selling it without having to move out. Therefore, if you sign the contract, you lose the apartment. If you don't, you lose the apartment by being cut out of his will. Either way, the apartment is gone.