The mom thing doesn't sound so terrible. Typical elderly mom stuff. She is saying she loves you, in her own way. Instead of losing your temper, take a moment to reflect, and thank God in Heaven that you still have a mother.
Your druggie relative, however- I would go no contact with them. That is a nightmare ready to happen. Be glad they're in California and not close enough to you to do things like crash out on your back porch reeking of beer and mud, or break into your house, or rob you.
Your mom seems to be a victim of this relative. How much thought went into bringing her to you? How old is she? How is her health? How is her cognitive health? Does she live with you now? What about her home? Is it possible he robbed her before taking her on this cross country road trip?
Your mom is part of your new normal. She was left helpless with you. Her future is totally in your hands. It is a felony to abandon an elderly or completely disabled person. You must find a way to either take her home (is she able to care for herself there? can she handle the trip on her own?), or set her up either in your home or in a place of her own or supportive care home nearby.
Do not abandon her to this druggie ex con. That may lead to her quick decline in health and other things I do not wish to talk about.
Her nitpicking is her way of showing concern and love. I have my mother and ex mother in law who both remind me of things they believe I should change about my life, every time we are on the phone or in person. And it's because they love me. I don't take the criticism to heart. Because I know it's not meant in cruelty. Rather, I respond with love that I promise to take care of myself.
There are words from Crosby, Stills, Nash, and Young that I would take to heart, if I were you, regarding your mother:
Just look at them and sigh
And know they love you.