Too many ponies and someone needs to go!

Nice easy keeping mare that would be suited for an advanced beginner who is an assertive rider as this mare at times can be stubborn. We have used her for pony rides and beginner riding lessons. She had done a little jumping but mostly flat work. She has been on several trail rides with other horses but does not like to ride out alone. Unsure if she has ever been bred, we have owned her for about 5 years. Does not buck, kick, or rear, but does sometimes toss her head.