Breakingapart, you are heard. And I have been there. Strangely enough, not the reason I'm on SI right now. This happened to me with my first xWH, years ago.
Some random thoughts...
It's important to be the "rock" for your children. Stable, consistent, even-tempered, safe. No matter what. It's hard. And completely necessary.
If you are able to be the rock, the kids might go along to get along with the OW, but you will always be their mother and their safe place. Nothing trumps that. NOTHING.
Let them (WH and OW) keep the basics for the children at the other house. Clothes, toiletries, etc. Then you won't have the stench of it to deal with when they come back to you.
Trust in your children. They are in a tough spot. They love their dad, but this new situation is horrible to navigate. They are hurting. You've taught them to be polite, and they really don't want the OW around. But what can they do without being impolite? They know you are hurting. Imagine things from their perspective. Give them permission to navigate as best they can, knowing they love you.
Use the time the children are away to take care of YOU. Sleep. Watch endless Netflix. Exercise. Indulge in a hobby. Connect with friends.
It's so hard. I know first hand. Here are some things I had to let go with my first shitty divorce when my twins were only 4:
OW constantly bought new clothes for my girls. I was so f$^&ing broke, I couldn't compete.
OW took my 4 year old girls to the mall and had their ears pierced. When they came back on Sunday, I gently removed their earrings and calmly said, "Oh, well, your dad and I said you could get your ears pierced when you were 12 and OW probably didn't know about that. It's OK, you aren't in trouble."
OW and xWH often turned up drunk to pick up them up. I called the police once, which I hated to do, but I was worried about them driving drunk with kids in the car.
The kids' IC stressed the importance of maintaining a stable, predictable environment because of the chaos they had to endure with their dad. My girls are 30 now and they can articulate clearly the dysfunction they witnessed with dad and AP, and where their safe place was - with me. But I had to really work at not freaking out that the AP was in the picture.
Trust me, the kids don't want her there any more than you do.
Regarding custody issues...
College fund
Life insurance beneficiaries (you until the kids are of age)
Holidays visitation
Summer visitation (when kids are out of school)
First right of refusal
Adequate notice of right of first refusal
Health insurance
Payment for school clothes, pay to play sports
Pet arrangements (do pets travel with the kids?)
Notice of out of state travel
Who keeps the children's passports? (you, of course)
Notice required for doctor's appointments? Should he have the right to attend if you make the appointment and vice versa?
Piercings and tattoos - who can give consent (from personal experience, sadly)
Cell phones - at what age and who pays
Also echo suggestions around the COVID precautions mentioned previously.
Long post. Sorry. Just some thoughts which I'm hoping you will find helpful. Sending strength!
[This message edited by BentandBroken at 8:01 PM, November 23rd (Monday)]