Can I be kicked out of HUD housing if I’m mom’s caregiver?

The answer is yes. Under HUD regulations you cannot have someone living with you if you have filed as a single tenent. Your Mothers share of the rent is based on her living there alone. And like said, a background check is done on new applicants. You need to speak to HUD, like said, and tell them the situation. Your Mom could lose her voucher so do it now.

HUD requires criminal background checks. You can’t have eviction history or old unpaid utility bills and no history of abuse of any kind and no animals or smoking. No felonies and certain misdemeanors disqualify.

Take a letter from mom's doc that stating mom's health needs and that she needs the care.

So, what does becoming a tenant involve? Do you have an objection to doing that?

Is this a "note" or an official notification? Go to the local HUD office and find out what your options are.