Just tell them you have a routine that works for you guys. It's going to be messed up enough travelling to the UK with the flight and everything else. The last thing you want is to plan to be apart from your bub when they will potentially be out of sorts. You are happy to go with them for short periods of time (and give them time frames so they don't pick a window that will mean bub is due a feed bang in the middle if that) but your bub has to, and will, come first.

It's not fair on her to be left with her dad when he is her non-primary carer, away from her "normal" space, and with him wanting to catch up with a lot if people she doesn't know - so potentially being on show and expected to be happy and upbeat all the time.

I work and dd was at home with dh at that age - but even then, away from home, I'd have been reluctant to plan a full day away from her. I would have had to wing it when we arrived based on how she was faring as her needs came first. I know when we've been away from home dd has upped the feeds again as extra comfort, so you may find you are even further restricted if she needs you more due to the disturbances with the flight and new people...