You are in a very difficult situation at moment and xmas is next month. I would focus on the positive that you are seeing your daughter every other weekend.
Maybe you should consider if u can getting some midweek contact as well as your daughter will put a smile on your face say every wednesday for an overnight every week if u can do it. I know u dont feel like it but hopefully u got an understanding manager and if u can have a word quietly maybe they can be there for you. Nothing beats going back to work when you are feeling low as u can keep your mind off whats happening instead of thinking about it . also u can speak to your work collegaues short term about it etc .
Dont blame yourself about anything and concentrate on your daughter who will for sure keep you happy.