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The age of majority, meaning the age that the child is legally able to move away from home in New Mexico is 18. If he is close to turning 18 it may be best to just wait until he is able to make the decision on his own. If he has a while before he turns 18, the "dad" can go to court and file for visitation and or joint custody. I'm not sure where the real father fits in here, but if the stepdad has been with the child since he was two, the judge may grant him visitation at least.
Technically yes since he's not an adult or of legal age to make this type of decision. If the mother calls the police they may make him go home, they may let him stay or they may allow her to press charges against you. Most likely the first time, they may just make him go home, but if he continues to leave and continues to be found in your home, then she would be able to pres charges against you. Some places are more strict than others, and it's also going to depend on how much the mother objects.