Can I sue for moving cost's due to an uncontrollable tenant?
No, that suit will not work. You might be able to get out of your lease though, but it might cost you more than moving costs. See -- http://www.utcourts.gov/howto/landlord/
Under SL County's municipal code 15.32.050, a property owner must maintain the premise in a habitable condition, and there's a list of things that matter, but the daughter being quiet is not one of them. Sorry, but we've all had neighbors we do not like living nearby, but it does not provide a basis to sue. You may have to move to find peace. For the ordinance, you can see --
Then browse to Title 15, part 32.
This answer or response should not be considered legal advice, and does not create an attorney-client relationship. If you have further questions, I would be glad to discuss your situation further. I can be reached at US - (801) 746-6300, or online at -- http://www.lewishansen.com/attorneys/robinson.html