Hi, Jodi,
Agreed with the previous responses. Save yourselves a lot of inner city driving by renting at Glasgow Airport. It's a lot easier to get out of the city area from the airport, as the on-ramp to the M8 is right there.
The train journey is really delightful. If you have the opportunity, take the train that runs through Falkirk High. It's about 15 minutes longer than the southern route, but the scenery is better.
A car is a definite handicap in both Edinburgh and Glasgow. You'd have to find accommodation that had free parking, but even at that, you'd be leaving the car where it is, and taking public transportation or taxis everywhere. So you'd be paying for car hire that you wouldn't even be using.
You should be able to rent at GLA and return the car to EDI with no one-way dropoff charge. Assuming, that is, that you're flying out of EDI.
The #500 express bus from central Glasgow to the airport runs about every 15 to 20 minutes, and costs eight pounds. The car rental agencies are now in a separate area at the far end of the terminal.
Slainte!
Mike (Auchterless)