I would also watch the amount of milk intake, and make sure they are drinking lots more water than milk. I think by now your kid should be not having anymore than like 16-20 oz of milk in the day.

I worked with a dentist that specifically worked with kids for poor airways. Tooth pillow is a tongue and lip correction advise not specific to mouth breathing. It is not an expander, but its more around proper tongue position and behavior.

It won't work for some kids and you will still need an expander, but if your kid is young enough it could help.