As long as he is offering her food I wouldn’t worry. She won’t starve herself
He's offering food. She just isn't eating it. I noticed my wife has that issue and it's because our daughter always wants to play and they have their own ways of hanging out. So she will graze but even then, not really. But then she comes by me and home girl will eat a half a sandwich, a mandarin, and a half cup of like blueberries 🤣. I'm sure it isn't that he's just not feeding her. Shes 2. If shes hungry shes going to eat. She'll ask for food in some form if she isn't saying "im hungry" yet yk? I'd ask what it is he's doing during meal times and not come from a place of "i want to fully trust your feeding her but-" and more like "i know how hard it can be to feed her, especially since shes 2. I was wondering what your meal time routines look like so that we can see how we can maybe change some things around so shes not asking for food immediately at daycare." Yk?
Spend time on weekends preparing her meals together. Take turns preparing and serving her plates. He can learn from you and you can see what he's doing, how its different from what you're doing, and whether there are any major issues you need to address. You can also give him feedback. Maybe your daughter would like a special new set of dishes she uses with daddy so she breaks old associations and starts fresh. Maybe she'd like a table that's her size, or needs more time to eat before leaving for daycare. Maybe she needs a different afternoon routine, or different food options. Lots to try here. Stick with it and give her some more time to adjust.
I need your tips...my daughter eats like two bites of whatever I make no matter what it is.