You don't have to tell them to fuck off, or do anything extreme, in fact you don't have to do anything at all for them.. it's easy to do nothing, stop trying to win their approval as they will never give it, it's a pipe dream.
You say your partner is a pushover, well he's dealing with years of guilt and mental abuse that he is fighting against every time they try and guilt him into doing something, if he hasn't got you standing in his corner being the voice of reason and support, then what is he supposed to do? He has no choice but to back down as he always has.
I would never tolerate this for my partner and child, dangling carrots like they do.. you do realise that is the only power they have to control you with and you're both lapping it up, your partner is still believing their bullshit, you don't seem to believe it but won't stand up for your partner? It's like you're both waiting for any scraps to come your way, while simultaneously being jealous that his brother and sister get more than you and raging against the injustice of it.
Don't think for one second that the brother and sister have it great.. you trying to get the moral high ground over them is exactly where the parents want you to be, but they are being coerced too just like your DH, but at least they've learnt how to make it worthwhile for themselves.. and you're judging them for that!! Being the martyr benefits no one in this scenario.
You both need a long hard look at what you're doing here, by all means let your DD have a relationship with them if that's what she wants, but once you remove all their power and control from the situation you will be much happier people.