Ang....This sounds like a fairly unhealthy situation. Are you looking for understanding? sympathy? advice? opinions? I'll list my comments for you. Do what you will with them.
1. Your husband can't MAKE you do a damned thing you don't want to do....You're an independent adult with a brain & conscience, right?
2. If you honestly feel your husband believes his son (typical & expected) let him believe it. You know the truth & know you did not do what his son accused you of, so let the kid say whatever he wants.
3. When his son comes to your home, isn't your husband ever there at the time?'
4. Have you ever indicated in any way that you resent or don't like his son?
5. Is your husband aware of the "trouble" you claim this kid gets into....and does he not communicate with the boy's mother about these issues?
kicked out of school, lying, stealing...sounds like a teen-aged punk...seems like Daddy may be in denial.
6. Lock up your valuables & private effects and when Daddy's pride & joy comes to your house.....LEAVE. Go shopping, visit a neighbor, go see a movie, but just do not be there. Don't subject yourself to false accusations.
When and if Daddy comes to his senses & apologizes to you....resume your normal activities in your own home.
7, Should this child cause additional strife between you & hubby and your husband repeatedly takes his son's side, being totally unfair & disrespectful to you.......if I have to suggest to you what you need to do, frankly, I'd have nothing more to say....except if you're into mental & emotional cruelty, abuse & victimization....stay with the jerk & his punk son. If not, grow a spine.