As a person using an older, underpowered laptop (cheapie from Wal-Mart that came with Vista and crapware, downgraded to XPXP3), I very much appreciate all the work you do to keep the software running smoothly on such computers. I also agree that it would be unfair to withhold features just because some people might not be able to use them without slowing things down too much. I try to make it clear that whenever I suggest a feature, I mean it should be optional, but if I forget, please assume that I mean for any feature to be optional, if possible.
I don't think you need to worry much about what other cars are doing in the pit lane. As Grunz said, if you see a car cross the sensor when it's still in the pit menu, start a timer (user configurable) and any car detected passing the sensor before that timer expires will get a penalty.
For what to do when that happens, if possible, make them optional, but if that's too complicated, I'd be fine with:
Fuel: stop at current tank level
Tire: Can it be treated like a tire wear level? If switching to different kind of tire, just give it to them. I would consider this part of the penalty to the driver that pushes the car. They just gave the other can an advantage by pushing them out of the pit lane. As pit lane strategy can mean a lot in a race, it rarely behooves the pushing driver to give the other car fresh tires without the necessary delay.
Repair: stop at current level of repair based on elapsed time. Maybe like Tires, give them full damage points back.
Stop&Go: cleared. Just like Tires, the pushing car is put at a disadvantage because he was impatient.
IMHO, giving the pushed car the benefit in such a situation will be a strong deterrent to those who would consider pushing them out of the way. While they might get out of the pit lane sooner, they'll just have given the other car the upper hand with no penalties or damage to clear, fresh tires, and heck, maybe even a full tank of fuel.
But, that's me.