I've seen so much misinformation on this subject recently on various threads.
Children can travel between parents during lockdown yes. But this does not apply when the child has been told to isolate. They should be staying at whichever home they were at when told to isolate.
Yes it's shit. Yes it's unfair that one parent would have to take 2 weeks off potentially. But it doesn't make it any less true.
And no, if your child tests negative it doesn't mean they can then go. The isolation period must be completed at whichever house they are at.