There is nothing wrong with knee high socks or stockings. They don’t have to be full pantihose. But here is my recommendation. Make your changes slowly. Gradual acceptance of standards makes for a) a more permanent change and b) greater acceptance by others.
You yourself recognize this when you say you don’t want your mom to think you’re going “all BP on her,” (whatever that implies). You avoid that issue, by increasing bit by bit what you choose to change.
There is nothing wrong with regular stockings. They don’t HAVE to be black or thick. Your skirts have to be long enough to cover the subject properly, but regular socks may be perfectly adequate halachically in someone who wears a long enough skirt.
I know there are many who would advise you, just go for it, wear the most stringent cover up for your legs that you can. But you asked for advice on how to accomlish this without upsetting your mother, whose kovod is unquestionably important to you. I believe the best way to do that is by “desensitizing” her little by little. JMO.