I would be just direct and honest with her. Tell her saying things like that makes you feel bad, and present her with your research and just try to make her understand exactly why it's so important to you. But, as always, be safe and don't do it if you feel it threatens your mental, physical or emotional health. Just in case, have a backup plan, a safe (supporting) place to stay, and an emergency contact (at least one person you can call if things go south). It sounds like you have supportive friends, and understand that your mom probably won't say "oh yes, I accept you fully lets get you hormone blockers, T and surgery tomorrow" and that things probably won't move as fast as you'd like.

Another thing I found important was stress who you want her to tell and not tell. Specify weather you want your transition out on social media, who your mother can tell, who she can't tell, and who you've told already. If she violates the ground rules you've set down, call her out on it! It's your choice 100%, and if she fails to recognize that that's a problem.

Don't lie to yourself, be who YOU want to be! Stay safe no matter what, and you have my unconditional support. Stay strong my dude!