Hey hurt turtle,
Since you helped get me into surfing 12 years ago, and since you brought it up on a public forum, I thought I would offer my advice/observations. An added benefit for you is that if I'm way off the mark then you will know

Firstly I would suggest that you sort out when and how often you look after her kid from another father. Since you weren't allowed complete parental control of him (weren't allowed to discipline him) when you were in the relationship why does she expect you to be his parent now that you have broken up

You were willing to assist in looking after her first child. Good on ya! More power to you. It's a noble thing. Let me relieve you of any guilt though. You shouldn't be under any pressure to care for her first child just because you were a good bloke while you were with her. His father should be bearing that guilt, not you.
It's your decision whether you want to have a father type relationship with him or not. Of course it would be a good thing if you do decide to kick the ball or hang out with him regularly. Keeping in mind that you definitely have an obligation to look after you own child, how many times a month and when you offer to be his mentor on top of that is completely up to you.
Story time: My wifes friend (who is female) got divorced. 2 of her kids were her ex-husband's and 1 was from a previous relationship (the guy from a previous relationship offered next to nothing financially or emotionally to his kid in 12 years). Anyway, through court process, etc etc, her ex-husband ended up with weekend and wednesday evening 'parent time' with his 2 kids. Even though it was a long bitter court process, he persisted in regularly offering to care and parent the older child that wasn't biologically his
! By doing this he earnt alot of quiet respect.
If you believe that you do want to be in the child's life long term, and not just keeping the ex happy for now, then put some time aside for him. Maybe spend a couple hours with just him every second Wednesday (or whenever suits).
Now on to my second piece of observation and advice...