
Now that sounds a bit better, and probably cheaper. But the only thing a PS reservoir and transmission have in common is in some vehicles they use the same type of fluid in both systems. I haven't looked, but do our cars have a separate reservoir for the PS fluid, or is it part of the PS pump? Hopefully they won't have to replace the whole pump.
One bad thing about many of those oil change type of places is they try to sell you additional services because it means more profit for them. It is possible you could use a transmission flush, but if you have a lot of miles on it, a simple fluid change would probably be better. Both of our Vibes have about 55,000 miles, and I plan to change the trans fluid on them around 60,000 miles, but probably not flush it.
Good luck on it and hope you find a good shop to work on it. Sometimes asking friends or co-workers will help you find a good place that they use.