I want to keep my characters house but not the character, she is a non-mayor and her house is big, but I want another character for that house
Can I do that?
No. You can't keep the house and delete the character. When you get rid of her house, the character is deleted altogether.(someone else should expand this answer as I can't think of anything else to put here)
If someone moves out, their home disappears. If you want to keep the house, the best strategy is to remove everything from the house, put the items on the ground and pick them up on your mayor character. Then, once you delete the non-mayor character, you can let a new character move in at the same spot of the old house. Until you get enough bells to restore the house to it's original size, just keep your old furniture in the rooms you have for now or leave them in storage.