Your mom sounds like she's just being...well...non-supportive

There is no logic behind her claims, whether she knows that or not. You can't be jailed for using the men's washroom, nor can you legally be arrested. The worst they can do is as others have said, which is to get you escorted off the property.
As far as I know, no western nation has any law concerning washrooms that aren't attached to indecency laws...so unless you're going to parade yourself around the washroom in the nude whilst making sexual advances on everyone around you, you should be ok!
At best your mom seems like she's either paranoid or just isn't supportive of your transition. But you don't owe her your own misery. From the sound of your post you've been doing quite well in living your life as your true sex/gender. Don't let her ruin that for you. Do your thing and be yourself, but don't give up.