What if one of the parents refuses contact? Should you strive for it?
This is a question of law. In some places, the laws will allow one parent, or even no parents, since it's a matter of religious preference. In other places, the laws are strict, and require both parents' permission.
This is also a question of the sangha's policies. Most will have an age limit because they observe a need to gain life experience. Some will permit children, and others will even seek after them, so that children will not be unduly influenced by outside ideas. So it depends a lot on who is asking, and who is doing the ordaining.
Ordination can be a big deal. Mostly, though, it's merely feeling a call to serve others, seek the best interests of the world and promote its well-being. Nobody needs an ordination for that, but it helps to have a legal piece of paper to avoid certain troubles.