6 Year Old Havanese Biting Problems

[Alix.marie]

My mom has a Havanese names Bijlee that we adopted about 3 years ago from another family.
When we first got him we could hardly touch him, he hated kennels, and he constantly growl and try to bite when we tried putting his leash or collar on.
Over the years he's gotten better, but he is still doing his business in our basement, although he knows to go outside.
My mom is able to pick him up now and whatever else and he's completely fine most of the time, but right when she thinks she can trust him he bites her although he's let her pick him up or whatever a million times before. He's bitten my sister, my dad, my auntie, and my grandparents before too for doing things they normally do like put him on their lap when he begs to come up, or things like that.
He's get aggressive with our other Schnoodle, Daisy, as well when ever she goes near where he's sleeping or laying.
My mom does not know what to do and is afraid she's going to have to put him down if he bites one more time.
Is there any reason why he bites or continues to do his business in the basement? My mom will not let him up on her bed anymore, and is more cautious when petting him or lifting him up, but wants to know what else she can do.
My mom loves him and doesn't to put him down, but cannot put up with it.

Thank you in advance for your help,
Alix-Marie