Health Insurance - Child Covered on Two Policies

I have heard of children being on two private health insurance policies and am wondering how this works in practice. My daughter's father now has another child so they have a family insurance policy. If he adds our daughter to his family policy and I keep her on mine, what are the practical and possible legal ramifications. If the policies are with different companies, could she possibly get access to both. For example, if she goes over her minor dental allowance on one, can she use the full amount on the other policy? I know that if you have some orthodontic work (like a plate) and claim it on your dental policy and then move on to another company, that the second insurance company reduces your allowance by your claim with the previous company, or at least that is my understanding. So I am curious how the more minor stuff works if there are two policies in play.

Thanks.