If the house has always been in her name, (specifically the deed), she doesn’t really need you to sign the quit claim deed; however, many financial institutions (banks) require a Quit claim deed even if your final judgment of dissolution of marriage awards the house to her for instance if she were trying to sell or refinance that residence. Look at your final Order or call the attorney who handled your divorce.
It would depend on whether your parenting plan established shared or sole parental responsibility. If you have Shared, then yes. You would need to at least consult with him on the issue. If he doesn’t agree, you can enroll the child, but try not to have it on occur on his parenting time with your daughter. He isn’t required to take the child tot he class or pay for it unless he agreed to her enrollment. Most parenting plans require that if the parent agreed to the enrollment, he/she must take the child to the activity. If you have sole parental responsibility, you can enroll the child without discussing the matter with the other parent.