Which mosfets you would use would depend on how much current you expect to run, and if you can handle using surface mount parts.
I'm guessing you will not want to use surface mount parts, mostly because they tend to be difficult to use without making a PCB. You could use something like the
IRLR3714, its on resistance is very low and it will handle very high currents. You'd probably want to use a simple switching transistor on the 2.4v input so you can use your higher voltage battery supply on the fet gates. You could do this with your relays too, so you can get enough power to turn them on.
To do it with mosfets you could build a full h-bridge so you can have forward and reverse, which would take 4 mosfets (preferably 2 n-channel and 2 p-channel). If you just want to go forward one will do.
If you are only pushing about 1A for the motor you could use
this H-bridge IC.
If you want to stick with the relays you can use a transistor on the 2.4v output from the car to switch the 7v battery to your relay coil to turn it on fully. This is probaby much less trouble than using mosfets since you already have the parts. runtime won't be as good, but I don't think your going to be too concerned about that at this point
