"I feel as though they are not sympathetic to the fact that I only spend 8hrs a week (which is heartbreaking for me) with my son as he goes to his dads on the weekends"
If you've been talking to your new colleagues in this much detail about your personal arrangements I imagine they find it difficult to know how to react. If anything they may not want to express anything negative about your working arrangements as that may be perceived as criticism. How exactly have people not been "sympathetic"?
"And there is a office resentment because I start 30mins later because I want to spend that extra 30mins getting ready with my son because I hardly see him when I'm at home. I've been told that I will be getting a warning because I'm late"
This is two things. Firstly, assuming you've negotiated the later start with your manager, it does sometimes happen that people are resentful of these individual arrangements, particularly if they are using morning childcare or whatever. There's not a lot you can do about it, and I wouldn't react by trying to elicit sympathy, I'd react by just doing a great job and giving it time.
Secondly, if you've been told you will be getting a warning because you are late, that either means you've taken it upon yourself to start later because of your personal preferences, or you are coming in even later than the 30 minutes you've negotiated. Both of those are not on at all, and your reasons are not your employer's problem. Thousands of people with children work full time and are able to get to work on time.
The problem here isn't your employer, it's your contact arrangements. If you and your ex are both working full time, surely it would be fairer to have alternate weekends. That's what most people do isn't it?
I'd focus your efforts on sorting that out, and on making sure you are in ready for work at whatever time your manager is expecting you.