I sent my kids away and have taken kids. I wouldn't take a child that the parents keep on calling/facetiming and sending gifts. From my experience it makes the kid more homesick. I found that it was best if they became part of the family. If it was a really young toddler I was mommy to them too.
I never took kids above 6 so wouldn't know if anything is different once they're older
I also go visit the house they will staying by a few times and show them where they'll sleep, eat... so they are familiar with the place. I found it the most important with toddlers