@andrematrixxx
I suspect your Dad is distancing himself a little from whatever your SM might say. A bit naughty of him, but there you go! His way of protecting your relationship with him if the conversation gets a bit tricky, and leaving the hard emotional work to you and the SM together.
It isn't easy navigating the changes needed for this new situation. A new baby necessitates major change - life gets dominated by routines, sleep patterns (or endless waking). It doesn't gel well with the desires of a young adult for late nights, random meals, socializing, friends dropping in without notice etc.
At 20, you are really going to chafe at the restrictions a small child creates for the household. Putting your stuff away in case she picks a battery up and swallows it, not leaving household chemicals in reaching range, locking cupboards, closing stair gates - stuff you'd be instantly on the ball for, for a child you created, but less so for one you didn't.
I'm not sure that 'humiliating' is quite the right word here. For this to work, you'll need to accept that their world has changed completely, and be prepared to adapt around the whirlwind. Patience may be in short supply, and you be required to step up as an adult - clean up, cook, do laundry, sleep at sensible hours. Sticking to times agreed for bathtimes, doing laundry, using the kitchen etc
Is there a more palatable solution for you with friends perhaps?