When I met my H he was married with 2 DC but just about to separate (not due to infidelity on his part) and he left the marital home to move in with me. His children stayed with us 2 nights a week plus holidays until they were in their late teens. We now have 1 DC of our own but sadly are in the process of separating ourselves.
I am currently seeing someone else who is also married with DC, this time obviously the infidelity is his.
Having become a step-mother at a young age I am very wary of stepping into that role again and am more inclined at this stage to encourage him to stay together with his W (who does know about our relationship but doesn;t know me) for the immediate future. I don;t want to be the reason that he leaves, if he chooses to, and becoming a step-parent and stepping into someone elses' shoes is an incredibly difficult role to take on, and certainly needs a lot more consideration than I gave it first time round
Just because the relationship breaks down with your partner doesn't mean you stop being a parent in any capacity and the couple need to decide the best way of maintaining that parenting role.
In some cases I think this might mean staying living in the marital home, even if only for a finite period. In most cases at some stage obviously one parent has got to move out, so that both can move on.
As for falling in love, well, I did love someone who had children already, and now I have strong feelings for someone else who has too, and I think the infidelity bit is irrelevant in respect of the children, really, if it happens at the point where the original relationship has broken down to the extent of being on the point of separation.