The signature lines disappear once you log in but I think it is R2C's or AS signature which says "What is right for my kids is right for me ".
If your W was being difficult, using the children to manipulate the sitch and spewing rubbish about you at every given opportunity, then my view would be 100% with AS. Fight. Fight like nothing else matters because nothing else does.
But your W is not like that. She sounds, strange as it might sound, decent. So the question you need to ask yourself is "what is best for my kids". If you honestly think that having two homes can work, then fight for that. I have seen it work and seen it work well. But, the logistics do add complexity and, as you have seen, the fight will add stress to the delicate balance you and your W seem to have developed as co-parents. But patience and the love for your kids will make it easy to manage the logistics and you and your W will regain the balance in time (like I said, I think you are both good people).
For people like us, you, me, your W my H, it is never about the money and it is never about the fight. It is about our kids. Your W was willing to lie so you didn't have to pay maintenance. You were willing to give up time with your children so they could stay in their home.
As for what happens when OM or OW enter the picture. Well, I like to think that my H and I know and respect the other enough to get past that. My H will always be my childrens father, whether he only sees them on the weekend or has them 50 pc of the time. I will always be there mother. We respect each other enough not to let someone else take on those roles. We are their parents. This will never change.
It is not how much time spent we spend with our children that makes us parents. Both of us would drop everything to be with them. When we are with them we are with them. At least one of us is at every school event. My H once refused to fly a plane because there was a lock down at D9's school and the school wouldn't release why. He would not take off until he knew she was safe. (Turns out there was a man seen with a knife in the school down the road. D9's school locked down as a precaution).
Again, ask yourself. What is right for my kids. What type of woman is my W. Ask yourself this question honestly because only you can answer it.
As an aside, my H was raised by a stepdad. His parents D when he was 11 and his stepdad moved in a year later. His biological dad was the kind of dad who would call up 10 mins before pick up and say he wasn't coming. My H has never considered his SD his dad even though he was around 100% of the time partly because his mum never encouraged him to. His SD is a good man (my kids consider him there grandad) but it was clear to him that he was not their dad - MIL raised the kids, she disciplined them, she gave them cuddles when they were sad and helped them through every minor and major decision. MIL made sure H knew who his dad was even going so far as to make excuses for him "he is stuck at work", "he isn't feeling very well". My H idolised his dad until he was well into his 20's (when the truth came out).
