1) Is your LG going to be charged for criminal offense as child abuse?
2) Are you and LG going to lose child custody?
Both of above greatly depend on how you usually treat your daughter. One single case of physical punishment with a few blacks left on your daughter will not endanger anything and you should be honest and sincere. Your daughter's statements are not important. But if the abuse is not just this single case, you have no other choice but to consult a lawyer, and do not say anything voluntarily.
If it is just a single case of physical punishment,
3) How to continue loving your daughter while keeping her in boundaries? Consult child education experts, read books, join parent connections, learn from friend.