Mimi..this is my take:
If this guy was a girlfriend and she asks about your kids and sends her love, what is your impression and rationale? Just a concerned thoughtful friend right? So why do you not accept that guys could be that too?
Don't be too cynical about men in general just because your first relationship did not turn out to be ideal. Give men a chance and let them surprise you. I think there are lots of men who adore children and would not mind being surrogate dads to other people's children.It is a good thing and as a single mum you should be pleased with the fact that there is a man in your life who cares about kids.
You don't have to be over sensitive about it and feel that he has a private agenda to impress you. BY all means encourage him to meet with your kids and that is the best time to suss out and observe whether he is just putting up a show to impress you or he is genuinely fond of kids. If he is interested in you and loves you he ahs to love the entire package that you represent or else there is no deal..