...the rear motor probably draws 1 to 2 Amps.
Probably? Have you measured it? If not, you want to do that first. You want to measure the total running current draw, as well as the current draw when the motor is stalled; when stalled, the motor may pull quite a few amps, depending on its design.
If you don't still have the original receiver board (as mentioned, this would be the best way to go - see this mega thread for ideas: Arduino Forum), then you'll need another h-bridge solution.
If the motor really doesn't pull more than 3 amps stalled, then you could use an L298 in bridged mode (read the datasheet on how to do this), which will give you up to 4 amps (you need a heatsink for the chip, though - they sell cheapo driver boards on ebay out of china that have a heatsink fitted, but you may have to mod the board to use the bridged mode of the L298). If it pulls more than this, then you'll need to use something else.
Pololu (http://www.pololu.com/) may have what you need. You didn't mention the steering system - were you going to use the built-in method (usually another small motor driven by an h-bridge or an electromagnet system)? If you are, then you'll need another h-bridge for that (and you'll need to measure the current needs there as well); you might find that the current motor driver you have is powerful enough.
What would be better for the steering, though, would be to add a standard R/C servo to drive the steering; if you do this, then you might also look into getting an R/C ESC (electronic speed control) for a -brushed- motor, and use it to control the drive motor. That way, you can easily control the platform using the Servo library. Most ESCs these days, though, tend to be for brushless motors (which won't work for your motor). Also make sure you get an ESC with "reverse" mode, so you can drive the motor in both directions (some ESCs are single direction only, meant for R/C airplanes and helicopters).
Note that ESCs tend to be rated in the number of "cells" they support (NiMH or LiPO cells); figure approximately 1.2 volts per cell; so a 5S ("S" for "cell" - don't ask me why - maybe homophone reasons?) ESC is meant to control 6 volt motors; you'll find 6S (7.2 VDC), 8S (9.6 VDC) and higher out there as well. Make sure you get an ESC that is as close as possible for your motor voltage (whatever battery it was originally using will tell you). You can go a little over, but not much (not more than 25%, and even that will cause the motor to have a shorter life). You might also find them with integrated BEC (battery eliminator circuit) - some of these will be 5 volt, others will be 6 volt; if you can get a 5 volt one, you can use that to power your Arduino (bypassing the Arduino's on-board regulator, of course). Otherwise, if your car's battery is 7.2 or 9.6 volts, then just split it directly off to the barrel connector and let the Arduino's regulator do the work.
Hope that helps.