Fact: That woman sucks at raising kids. My awesome girlfriend had her son sleeping in his own room every single night at 2 (we started dating when he was 2 1/2). Hell, he wasn't even 100% potty trained when he turned 3, but at least he sleeps in his own bed, no exceptions, if he has a nightmare we'll comfort him in his own bed.
Boys, I believe, need boundaries set, they need a structured, stable environment to grow up in, they're going to push those boundaries and try to get away with as much as they can... So he knows certain things his mommy will tell him not to do, like jumping on the bed, but he'll keep pushing it... but when you get super stern about something like running into the street or holding hands in the parking lot, there can be zero tolerance for misbehavior, because that's how children learn right from wrong, ie: morality. She has basically raised him as a friend instead of as a parent. He is fucked for life.
I guarantee sleeping in her bed at night is only the tip of the iceberg in terms of behavior she has tolerated/allowed for his ENTIRE life.
Are you incapable of having children of your own? Do you not want kids of your own someday? Would you really want this woman fucking up your children as much as she has already fucked up her own? He's probably fucked, even if you love this woman, I'd suggest breaking ties. I dated women in the past with older children, it's a headache and difficult situation to begin with, but none of them were as bad as what you've described.
Don't necessarily discount all women with children, if you're looking for a potential woman to raise your own children, it's nice to be able to see how she's handled one on her own... because it does get easier with 2 parents, but if she can't handle it solo AT ALL, then you should move on and find a better option.