it's just my mom doesn't think that an instructor is necessary unless I really get serious.
An instructor isn't necessary unless you want to get
What I'd do is try to talk the moms in to doing like a test run: let me take 1 or 2 lessons and then let's sit down and see how well it worked for you; are you learning new stuff quickly, are you feeling more confident, are you able (after the lessons) to start developing new skill independently on your own time, etc.? If you answer yes to these questions, then the instruction is really paying off. If not, see what you can work out on your own after and see how that goes.
OTOH, if after a few lessons you're not making super rad progress, maybe you need to reconsider. Not trying to rain on your parade, just saying that if you're not seeing instant results, take a time out and work on stuff on your own (after the lessons) and see if you can put all the pieces together and make more improvements that way.
Either way you're not really asking mom to commit to a really big investment off the bat, but your'e leaving the door open to more
lessons if you can show they're working for you.