I think the timing is VERY deliberate:
FD has the kids for Saturday, by prior arrangment. It’s also a long weekend so there is an extra day to deal with possibly having the kids.
If JD “disappears” on Friday, FD can be there to pick up the kids so they are not alone, as he is going to have them on Saturday, anyway, correct? Then as JD is still missing Saturday, and Sunday, and Monday, and even Tuesday, he keeps them safe at HIS home. See the logic?
Then he has possession and will be keeping them while LE searches the Wavenly Park for her, assuming the ploy of her assaulted while jogging is believed.
The key for FD is to get his home cleaned up enough to make sure it is ready for the children, once a missing person alert goes out on Friday evening. And hence the rush to get it all cleaned up, to dispose of her body and all the bloody clean-up stuff by 7 pm. It really bothered me that FD and MT were driving through disposing the 30 bags in daylight, not at night. If he had to be home and available right away to get the kids, it would answer why this all had to be done so fast.