I'm late to this one...and I'll admit that I have no personal experience as I'm still married...but...
At pushing 40, I've now seen my fair share of dating/remarriage relationships catch on fire and explode because of previous children.
It all depends on the woman, but I saw earlier that someone said the kids will make/break the relationship and by what I've seen, this is 100% correct. If the woman is more loyal to her children than she is you...and if those kids decide that they don't like you, you're screwed, it's over. One of the dumpster fires is a good friend of mine that I know to be a great person. For some reason or another, the children of gal he was dating decided they didn't want him around and in short order, it was done. In my age group, the children are 5-15 years old tops...and that is a BAD age if they do not like you.
I'm glad to say that I do not have to deal with this, by what I've seen, it is not something I'd want to go through.