If there was an agreement, even an oral or verbal one, that the family member would do certain work in exchange for a certain sum of money and he has not done the work you paid for, you could sue him to recover some of what you paid him--basically, that amount or portion of the money which he has not "earned" since he has not done that portion of the work. If he damages your home or leaves it in such a state that you have to incur higher costs to finish it (e.g. some of his work needs to be redone by another contractor) you could sue for those costs, too. You cannot force him to finish, though certainly he can offer to finish to settle the lawsuit (as an alternative to paying).