Ok so child arrangements are being done amicably but she still applied to CMS for child maintenance? She could have done that amicably. What you want really is a 50/50 shared care consent order which means there is no child maintenance to pay and you share the care of the kids equally. But maybe you can't manage a 50/50 arrangement (that would be every other week-end plus two consecutive midweek overnights and half the holidays).
When you say she got the house and the car and the kids, was that by amicable agreement also? If and when finances get sorted you should at least get a share of the house equity (assuming there is some). The starting point for that is 50/50.
I am guessing though, that if you've had a bill from CMS, that your ex has gone to the CMS to ask for this - which is not particularly amicable. She could have agreed a "family based arrangement" - ie informal like the child arrangements. Whereby you agree an amount of CM (if any) and who will buy what. Eg you might agree a lesser amount and agree to buy certain things or share the cost of certain things.
But - giving her everything does mean you will be liable to Child Maintenance! If she asks for it. The way the law works on that isn't fair. As Resolute says, if the kids "live with" her then you have to pay CMS at the assessed rate (especially as she seems to have asked them for it) because she is the "resident" parent.
There is no trade off between house equity and child maintenance. I suspect if you objected to anything financial she wouldn't be so amicable over you seeing the kids.
So I think you need to get the child arrangements formalised legally. You're probably being assessed on every other week-end only if the other nights are ad hoc. The amount reduces by the number of nights a week you have with the kids. Once they are equal nights and if there is a consent order that says the kids live with "both parents" (as opposed to live with her and spend time with you) then there is no CM to pay - and the rest of the financials are worked out as part of the divorce.
So do you think she would agree to a consent order for Child Arrangements? A consent order (not the same as a consent order for divorce) is a Child Arrangements order without the need to go to court. You would both need a solicitor. Yours would draw up the order, hers would approve it, and it would be sent to court for sealing. Once you have agreed the child arrangements,
If you're happy with every other week-end, half the holidays and one midweek night then technically you could ask for it to be "lives with both parents". Usually it needs to be 5 nights a fortnight for that (eg a 3 night week-end and 1 midweek night). But even then there would still be some child maintenance to pay as it's not 50/50 (but lives with both makes you more equal and means you don't need her consent to have overseas holidays and she is not the sole "parent with care".
Sounds difficult - if you want to keep it amicable and informal then you'll have to pay the Child Maintenance. Do you live at a distance? Or close enough to do midweek overnights? How many children? And are they all under 11?
It's not a fair system. Your ex could be earning a million a year and you'd still be eligible to pay CM at the assessed rate!
You also need to tread carefully, as although it's amicable now, she could change her mind whenever she wants. There is nothing legal in place. Eg if you don't agree to everything over divorce finances, she might withold the children (which does happen) - then it would cost you money to go to court to see them again,#
So I wouldn't straight up ask her to do a consent order for 50/50 - she will probably have had legal advice already herself and know what that means.
I'd suggest you start mediation in case you do need to go to court. It's a requirement to have had a MIAM (first mediation appointment on your own). A MIAM lasts for four months if you need to apply to court during that period.
So the options are:
1) Have the MIAM on your own and don't tell her.
2) Have the MIAM and agree to the mediator asking your ex to attend the next session (often the ex declines or keeps cancelling and they guess you might apply to court).
What we usually say is - don't move out without a Child Arrangements order in place. ie secure the child arrangements formally so the kids can't be used as leverage over the divorce finances - and to make sure the kids have stability.