Haircut confusion

You can braid layered hair. Its just that it all strands wont be neatly tucked in as with no-layered hair but nonetheless, it's braid-able.
Elbow length is still long enough. It's not like you're chopping all of it off.
If you want to keep the same length and want a slight change, just have 2 layers done. One framing your face and another about shoulder length. This way it'll be easier for you to braid, pin and handle your hair.
And of course, your mother will be happy too.