What is the ruling on a husband's vow to send the maid back to her country if she touches his child, and is his vow considered misplaced?

There is no basis for a vow to prevent the maid from touching your child, and there is no harm to him in that. This vow is not one of obedience, so you are not obligated to fulfill it. It is more prudent to offer an expiation for an oath (kaffarat yamin). If what you uttered was an oath by Allah, then this is an oath, and what you should do is break it, based on the saying of the Prophet, peace and blessings be upon him: "Whoever swears an oath, then sees something else better than it, let him do that which is better and offer expiation for his oath." You are required to offer an expiation for an oath: feeding ten poor persons, clothing them, or freeing a slave. If you are unable, then fasting for three consecutive days is more prudent.