Ok, I'll try a slightly more constructive post.
DP & I try to do nice stuff with his 2 dc & my 2 dc. Every time we go out his dd (8) acts spoilt e.g won't join in, won't eat same as everyone else, sits with sulky face on for hours.
I'm sorry, why should she eat the same as everyone else 
? The food this girl eats is one of the few things in her currently upside down life which she can control. Also, where do you sit for hours? If I had to sit somewhere for hours I would be pretty grumpy too, she is just a child.
It's really irritating me & one of my children (older - so realises what's going on) is beginning to say they don't want to come along because they know what dd is like.
Lol, lol, lol, your dc sounds like the petulant and intolerant one. The apple doesn't fall far...
He does really well & doesn't give in
Good boy [sarcastic]
but this usually leads to massive stand off which spoils it for everyone. Aibu?
Yes, yes, yes!!! You are bvvvu.
Any tips on how to manage this?
Mhm, let me think. Well, learn some compassion, accept your dp with his family, he comes as a package, try not to create a us and them family scenario. Also let your dp spend enough time with his dc alone, without you and your dc. Doesn't sound like it's a 'happy families' situation, so let them spend time alone. He is their father fgs, he is more important for them than he is for you, you better get used to that or maybe, as someone else has said, blended family is not your cuppa tea.
I can't bear to see him being manipulated like this!
Well, others have already commented on this. But I interpret this comment as you being cold, selfish, jealous and absolutely freaking over dramatic.
Hth.