Damsel, I have no experience of this specifically. But...
As a stepmother, I encourage my partner to spend time with his kids alone - infact tonight, my partner has taken his son (who's here for the week) for a meal and to the cinema - my suggestion. If your ex can keep some contact short, say a couple of hours, I see no reason why your ex's partner or at least your ex should not wish for this too. I'm sure his partner can find something to do for a few hours once in a wile.
As a mother, I wouldn't force my kids (as long as they can let me know how they feel) to spend time with someone they're not comfortable with. Your ex spent 3 years out of face to face contact with your daughter - so he needs to take things slowly and rebuild a relationship (and maybe bond) with her. When my daughter didn't like staying with her dad, I asked him to come over and read her a bedtime story and they slowly rebuilt their relationship. Even now, she sometimes doesn't want to go off with him, and we don't make her.
Another perspective - my mum left when I was young, and moved on with her life. After little contact with her, and over time, I felt no bond and to spend time with her would have been like tolerating hanging round with an almost stranger. That needs to be sorted out if that's the case for your daughter. Also I can understand your daughter not wanting to rebuild a relationship with her dad while there's another stranger in tow. It's hard enough as it is.
I understand your ex and his partner wanting to do things together, but I think they should be fair and give the situation time. Why should it all be how the adults want it! I guess your ex hasn't told his partner how much rebuilding of a relationship (and possibly bond) with his daughter he needs to do. But, that's tough! In the best interests of your daughter, I'd insist he works on that first. Yes, he's got to travel abroad and it's costly and limited in terms of time, but in time, if and when he builds a father - daughter relationship, he will be able to spend more time with her. It just sounds like your daughter's feelings are not really being considered by him. He needs to take things more slowly and involve his partner now and then in some activities, not 100% of the time of each visit.