Baby won't sleep unless father puts her down

[TinLizzie12]

I've been putting her to bed since she was born but since she had her sleep regression around January, she won't go to bed unless her father puts her down. Every attempt I make results in immediate crying and screaming, regardless of the method. She knows I'm trying to out her down and immediately resists. I'm not sure what to do about it. Her father works until 1am so she's been falling asleep 00:00-2am every night for weeks.

Does she sleep in later in the morning? Then I would think it doesn’t matter.
If you feed to sleep, does that work? If you can cosleep following guidelines, does that work?

A little but not much. She goes to sleep 4-6hours later than usual and wakes an hour later than normal. So she's missing out on 3-5hours of sleep most days. Often more due to not napping much.