First, yes, I would be annoyed by this. I'm not a single parent, but I am usually generally annoyed when people try to have their cake, eat it too, and then complain about the calories, if you know what I mean....
It sounds like this: no matter what your friend's situation is-- and this one is entirely of her own doing-- she's going to perceive herself as the 'put upon' one. She didn't appreciate her husband and is now POed that her actions have caused her to lose her 'built-in daycare'. My guess is that she has bigger personality problems than just taking her ex for granted.
Maybe it's time to have the hard conversation with her. Do you care enough about her children (esp. the two from the previous marriage who still likely love him very much) to have that conversation? Can you risk her being upset with you?
I find the whole thing a bit upsetting. I grew up with my mother behaving similarly and... well, she and I don't have a relationship anymore, lets put it that way. When people put their own momentary 'happiness' in front of the needs of their entire family-- I have zero respect for people like that.
And it sounds like you know what you are getting into and are willing to do the work of being a good mom to your son. I have two sisters who are single moms and work their butts off. Believe me-- I think they'd be appalled at your friend's complaints.