I feel that if he loves me like he says he does then he should feel and do the same. I think that being with a divorced guy with kids really depends on the situation. I include him in all aspects of my life: I got him on my softball team, he's met/hung out with my friends multiple times, he's met my family, I invite him everywhere. I am dating a man with 2 sons from his ex-wife and a daughter with his ex-gf.
A single mom won't want to spend a lot of time dating a guy who doesn't want kids, so let her know up front how you feel about kids and the possibility of become a stepparent, suggests Kate Anthony in her Your Tango article, “Kate's Tips To Be An Awesomely Datable Single Mom.” If you have kids, you might let her know you understand how challenging dating is for a single parent.
If the ex isn't co-parenting and the kids are too young to be left alone, she will have to hire a babysitter or at least have advanced planning to go out.
Money might also be tight for her, so offer to pay the sitter and definitely spring for all the other date expenses.
Dating isn't a single mom's top priority, so help her arrange things so she can get out with you.
Let her know you understand that her kids come first.