Asking your child to keep secrets from the other parent is never a good thing, not for the child & not for your custody case.
The other evening I was at Trader Joe's and saw a guy with his little girl who appeared to be about 4 years old. He looked to be with what appeared to be his girlfriend. The little girl had a cup and Trader Joe's was giving out samples of their coffee.
I overheard him say, 'How's your coffee?' I thought to myself, she's a little young to be drinking coffee and not only that it was about 6:30pm. The little girl said it was good, and he replied, 'Well you don't need to tell your Mom that I let you drink coffee, and he went on to say 'You don't need to tell your Mom a lot of the things we do together. And she said, 'well I don't tell Mom what we do together' and then he got on her case, 'Well you told Mom I let you watch DeadPool'
Now DeadPool is a really funny movie but it is definitely not appropriate for a 4-year old. But aside from that, what I really want to point out that putting a child in the position where they feel they have to keep secrets from the other parent, that is not good. And the reality is, they are probably going to go to the other parent and tell for example in this case, what the little girl did with Dad.
It not only puts the child in a bad position, it undermines the other parent's authority. It's not in the spirit of co-parenting. If this is doing this to your kids, asking them to keep secrets from the other parent. Stop. It is just not good for your kids.
What's important here is what's best for your children. It's always about what is in the 'Best Interests of the Children'. And I can guarantee you that if you end up in court and it comes up that you're asking your child to keep secrets from the other parent, the judge is not going to be happy. And sometimes it does come up, because the child's opinion may come up through some sort of counselor.
I was just recently at a continuing education legal seminar where some judges on a panel that said they actually talked to children about what it is they want and what's going on with them in the other parent's home.
If you want to do what's best for your children and what's best for your family & get the best results for your family, don't put your child in the middle.