This is the first question I’ve gone to answer where the person has a vegetarian family memeber – I’m amazed ^^ I think talking to your mother is the best step – do you live with her?
In all honesty, I think you’ve already got one foot in the door. If you’re worried about becoming a veg, then cut down your meat intake, bit by bit.
And in case you’re troubled by a previous comment, it might involve a few more vegetables to stay healthy in comparison to eating a steak, but it takes 10 plates of vegetables/grains to produce that 1 plate of meat, so don’t worry. (Plus there’s a dramatic less chance of cancer at the end).
If you think it is the right choice, then go for it ^^

I’m sorely tempted to say just stop eating meat.

Your mom is veg, so that’s half the battle right there. She’s already cooking vegetarian meals, so that problem is solved. Talk to her and let her know you want to go veg and why.

I’m actually vegan, and I know it’s the right thing for me. The only disadvantage comes when I’m eating with nonvegetarians, they want to go to a veggie-hostile place, and they think telling me to have a salad is good enough.

you really should talk to your parents about it.
you may need to see a dietician to make sure you are getting all your nutrients.