Asalam O Alikum
Well my English is not up to the standard but what ever i understand from your quote i want to give some suggestion to you.
First as you said "Yes I have made many many mistakes and a lot of bad choices in the past"
Brother your past is now become past and now if you did promise(tooba) that you never do bad things again and try to be a good man you are now pure as you never did these bad things.
Regarding your mom feeling/thoughts about you one thing keep always is mind , its your parent and you always to be polite with them even they say any thing to you you have to always be in limits and respect you parents.
I will suggest you to try to give your parents/family knowledge about Islam , first lead by example yourself and also try to remove their misconception about Islam .
For this you can give some Islamic book, or handle some lectures by some good scholar like zakir naik about similarities between Islam and Christianity , also tell him what Islam says about other prophets.
here is a link where you can find a good material
http://www.peacetv.in/
I pray to All-mighty Allah to solve any hardship you are facing.
Allah Hafiz