I;ve decided to stay anyway and work hard at making it work
This is the best news to come out of this thread.
Normally, I'm not so preachy, but since it was asked in the thread, I'm going to do it -- I'm going to write out my feelings on this issue as it is something I feel pretty strongly about:
I disagree with the majority of the responses in this thread. Once you have kids, one's own personal well being is secondary to the well-being of the kids until those children are adults. And, I'm sorry, but kids are better off with 2 parents than one. Unless there is abuse going on, if both adults can pretend to be civil to one another, the kids will be far better off than if they see a parent only the weekend.
If you need strength to live together, both of you should focus on providing the children with a stable household until they are 18. Sleep and live in separate bedrooms. Live next door if it has to come to that -- but it is really important that children have models of what responsible adults are like in their life.
Boys need to grow up with a strong male model to learn how a man should act. Such as fulfilling the responsibilities they have accepted. Girls need to grow up with a strong male model in order to know how a man treats a woman. These are the important things a father does. These things do not get ingrained over a few hours each weekend. They take years of bonding as the children mature.
And the above doesn't even cover the typical stuff that happens with children of divorce -- the parents disagreeing on discipline, the parents trying to one-up each other to be "the cool parent", and then all-too-often one or both remarries and either introduces step siblings or make new children effectively telling the old children they are less important. Etc. Etc.
Maybe your situation will be different. But statistically speaking, it won't.
It is my opinion that if she is willing to try again -- whether it is the 3rd time or the 333rd time -- I think your responsibility to the children says you try again. At the barest minimum, come to an agreement as adults to be civil with one another for the next 13 years until the last one is 18. Fulfill your responsibility as a parent. For every decision, ask "what outcome is best for the kids". And, since you are going to try again, may I suggest not to have another one until things have stabilized for quite some time.