This took an age to sort out because I could not get those red spheres to go where I wanted until I realized that I was going about it all bass-ackwards.
After the revelation and quite a few more restarts I was able to exit with all coins collected.
Here is a walkthrough for the first room of ButtonHole:
Exit red TP and take right coin. Jump to coin area and remove all coins. Enter yellow TP from the right and push sphere up, then down, then right again. Jump to button area and push sphere up. Exit button area and remove coin from ice. Push sphere down then down again. Exit the room via the yellow TP.
Yup that helped me but I'm just no good with maneuvering these spheres around. I'm sorry Michelle I just can't do this one. I got the first part but can't figure out the next. Guess we all have our weaknesses and spheres are mine.