Many ways. this one using Adobe Premiere
Put clip on timeline
rightclick video > motion
set start and end points of your clip to position 0,0 and rotation 90
OK
Render
Though I have to wonder how it is you are going to handle the aspect ratio difference. See your video has 2 sides. One is 4 units long, the other 3. Turn it on its side and now the 3 side is on the 4 side and the 4 side in on the 3 side. Messy.
You could simply stretch the sideways movie 'til it fit, but I think this is not a good idea.
You could shrink down the original long side to be as tall as the frame, and then fill in the rest with black. Not bad, but not good either.
You could crop it...
See, you're in a tough spot. Oh well. That's how to do it.
Better solution is to teach your mom how to hold the camera for next time. 