If this was your car, then I would say install whatever you want in there (no matter how ridiculously out of place it would look); However, this is your mother's car so in my opinion you should NOT install it anywhere. If you are just going to be talking to other nearby vehicles, then buy yourself a handheld and power it from the cig lighter.
If you insist on using a mobile CB, then mount it to a piece of wood (to make a base for it) and simply sit the wooden base on the passenger seat. If you will have passengers in the car, then make an "L" shaped mount that sits on the floor and rests up against the passenger side of the center console (use carpet. felt, cardboard, etc. between the vertical piece and the console to keep it from scratching), then mount the radio to the vertical piece. This will allow you to use the radio as if it was mounted to the side of the center console, without damaging the console itself.
Happy Road-tripping
