Kathy and Shawn Lewis, of rural Alhambra, have adopted out about 35 horses through their non-profit organization, Legendary Mustang Sanctuary. Alhambra couple rescues mustangs and burros | Belleville News-Democrat
Actually yes, all of your Constitutional rights can be taken away. This is made possible by the 5th amendment. The little part there about nobody can be deprived of life, liberty or property without DUE PROCESS...that's what gives them that right.
If your former spouse moves away with your child, and you have joint custody, you may be entitled to some relief. As mentioned above, Utah does not permit a custodial parent to move more than 150 miles away from the other parent without written notice and permission from the court.