I (M23) am a nightshift nurse, I work 12hr shifts 7P-7A, my work schedule alternates by week but follows as:

(Set 1)
MONDAY - WORK
TUESDAY- WORK
WEDNESDAY- OFF
THURSDAY- OFF
FRIDAY- WORK
SATURDAY- WORK
SUNDAY- WORK

following week is

(Set 2)
MONDAY - OFF
TUESDAY- OFF
WEDNESDAY- WORK
THURSDAY- WORK
FRIDAY- OFF
SATURDAY- OFF
SUNDAY- OFF

Set 1 starts again

On the first day off I usually get home about 8am and sleep till 2pm. I feel like a piece of trash and a “part time dad” because all I feel like I can realistically commit to is every other weekend(6 overnights a month). I don’t know how I can realistically have my son every single time I am off work, without sacrificing my health. I know parenting comes with challenges and sacrifices, but is wrong if I occasionally have the ability to get my son during the week like on Tuesday and don’t? Is it wrong if I use that time to just relax or take care of something I need to do? It’s not that I will never get my son, but I can’t PROMISE that I’ll be able to. My wife does not work and her parents live right next door and watched my son frequently when my wife needs a break.

A girl told me that was basically an absent father and wanted to “pencil in” my son when it was convenient. My wife was physically abusive to me, mentally abusive too. I didn’t want my son to grow up seeing that so that’s why I had to leave, I thought I was doing the right thing. Am I a piece of shit? Is my sole reason for existing now to just work sleep besides keeping my son? Am I not allowed to ever want to be an individual or date in the future?