@bondo Hey Man. We all feel you, we absolutely all had the ups and downs. I got a 2.5 year old and a 10 month old. I never had the terrible sleep like you, luck of the draw I guess. We did do a lot of what some would consider sleep training, but as many dad's will tell you, it doesn't work on every kid.
I feel you about dad bod, I was a fit lad now I'm a disgrace. I changed my mind set from looking good, to keeping fit. That helped. Instead of beating myself up for not going "all in" with diet and excercise. I give myself a pat on the back for going on a 6 miler once a week.
I get 2 hours on the ps5 a week with my bros. These are the little things that get me through it, it is a grind, there is not doubt about it.
The pay off isn't now, it's years from now. And I hope there is no greater prize than watching your daughter grown up and find happiness. At least I hope so!
Work in little rewards for yourself, work with your partner to get hers too.