You can't say "I'll ride you home." as the most natural interpretation is that you will climb onto your mom and say "Giddyup!".
You could argue that "I'll drive you home" would suffer from the same problem, ie that it sounds like you will get in your mom, shut the door, put her in gear, and proceed to drive her like a car. However, this is impossible, and so it tends to not be interpreted this way.
However, it is possible to "ride" someone - my son loves to ride on my back, for example - and so it could actually mean this. It's therefore more ambiguous.
There is also an alternative meaning for "ride" which means "have sex with". If you were in the back of a limo, for example, with a lover, you might actually say "I'm going to ride you all the way home.", meaning that you plan to have sex with them. So that's potentially problematic too, especially with your mom.