P.W.
Fighting is normal and although it is hard you should allow it unless you feel one is being overly cruel to the other, or it is going on too long. I know that is hard since you are hearing impaired but don't over worry it. First of all kids fighting is how they learn to work things out. If everything was all nice they would grow up not knowing how to compromise and not understanding that in fact life is NOT always fair! Try and let them work it out, although for your own sanity in the car I would assign seats. If they don't like it they will have to lump it and if there is too much friction I would just not let anybody in the favorite seat. Let them earn it......that probably would be more positive anyway..... or have a back up plan. Set them up for a little lesson. Have a babysitter on call. If they start up, call the sitter. Be sure the sitter isn't their favorite person in the whole world. Give them incentive not to whine and fuss. There is a parenting technique that saved me many times called "Love and Logic." Go out and buy the books!
One last thing. when my kids were younger there were times I would sit them apart and allow each to express their feelings on why they were upset during the fight......without the other child interupting. That was a major rule. Let them express themselves. They each get a turn. Then point out how they both have strong feelings, but let it go. Don't try to resolve it for them.
Good Luck!