Hi,
I used to be a homescholer and loved it, but now my girls are in school first and second grade as I had to return to work.
I also have a little one at home staying with my mother while I am at work. I really do not like public schools

But we still go on with piano lessons at home as much as we can in a home school style.
We too have times when they lose interest and then they like it again for a while and the they loose interest again....
What we did and worked and I can recommend is:
1. For all the chores they do, including piano, they get a certain amount of minutes that they can use to watch cartoons/movies or do a computer game. They could also choose other activities they like, but almost 100% of the time they choose screen time. For example for doing a piano game 10-15 min and playing a song double the times their age, they get 30 mins.
2. Over the time we have bought a blockflote and first I started to learn how to play it in order to display how learning piano can also help you progress in playing other instruments as well. After the blockflote we tried a violin which we boroughed from a friend and now we just bought 2 guitars (for the two girls) and we experiment on them. These are somehow making us use more time for music in our home. For example while the little 3 yr old plays "Hot Cross Buns" my oldest plays the same notes or chords on the guitar.
Hope this gave you a few ideas. And as for me I hope I can also find more ideas for my kids as well.
Best Regards,
Adeline