What's a good way to say "the front right 'side' of a car"?

In the motor industry, your problem is solved by creating the adjectival noun phrases:

Offside front, nearside front, offside rear, and nearside rear.

See, for example,

Specialist Assessing Services

In this commonly used nomenclature, your particular front right side (or corner) is the “offside front”.

For those who dislike offside and nearside, I suggest they be trivially replaced by passenger side and driver side.

You don't really need any word there at all:

The front left of A's car collided with the rear right of B's car.

If you insist on using a word, you can go with quadrant:

any of the four quarters into which something is divided by two real or imaginary lines that intersect each other at right angles