[Phalanx]

Lets just say...as long as sexually, things are not like "throwing a pickle down a greased wind tunnel" :D , and that the kids aren't involved in every SINGLE outing, every SINGLE occasion and likewise...etc...then yknow, a normal relationship wouldn't be unattainable to you.
I think the aforementioned points are a the main two things that a man , and respectively kid/s would weigh up.
Of course it goes without saying that there would have to be personality traits you like in eachother as well...

Oh, the whole "new daddy" thing, that'll throw a fella no matter how much he likes kids - Not saying this is you, but, it's what you see other guys shying away from.

As for the implications on the woman/family, well...as long as the ratio of time spent alone with kids, together, together with kids is on a realistic and reasonable keel, then all should go well.

As well as that (not saying this is the same in your case) but a LOT of women out of long term relationships I've known will tend to get quite lonely initially, making rushing into something with someone at a time you wouldn't otherwise a little more prone to happening...coming from the son of a mother who was pretty much rebounding one unsuccessful relationship off another throughout his entire childhood - simply because they hadn't learned to be alone, and work on themselves, well...it never really worked out for her, and I'd say the same for most.

Advise I'd give to all in these cases - Learn to be happy on your own, successful on your own, feel whole on your own, and move on from there...after that, who gives a fuck? - Don't let him run your child/ren, don't let your child/ren run him, and don't expect everyone to be best buddies, because when things like that are forced you may as well flush them from the get go.
Let everyone be themselves and adjust as comfortable/appropriate.