So sorry I have no solutions but just wanted to say I could have written this myself- totally in the same boat with my 2 year old! You are not alone!
We had this with my son as I usually did bed time and he generally prefers me however once I found out I was pregnant we had to get a bit firmer on the fact that sometimes dad does bed sometimes I do and it’s the same for if he wakes a night he gets who he gets. We had a tough night here and there (the first was the worst) but stick to your guns even if it means you putting headphones on or leaving the house. Your other half will find his own ways to do things as well which will help. Obviously you know her best but we found having a really clear boundary helpful.
Could you try bedtime/nighttime wakes with both of you for a few nights and then transition to just him? My 3year old is difficult if my husband puts her to bed but Ive taken a step back the last 2 months and now she will go to sleep for either of us, just takes a bit longer if it's him as she prefers me to do bedtime