Great to see such young passion for the instrument...and obviously a tolerant family. It sounds bad for a while.
I believe the reason most teachers do not want to take very young students is because their teeth have not set in at that stage. So any pressure applied may cause permanent teeth issues. Perhaps speak to your dentist as well.
I would take the opportunity to introduce music via a keyboard/guitar while teeth issues are in the equation. Usually 9 to 10 is a great age for brass.
There are a lot of good teachers on this forum, so listen carefully to their advice.