no need for all those thanks.
If the pull started after they mounted the tires then I'd suspect a belt issue in the new tire. Particularly since you already had one like that. To eliminate that rotate the tires, front to back and vice-versa. If the pull goes away, you know it's a bad spot in the tire. (Obviously the tire shop should be doing this, not you, it's their problem, not yours.)
FWIW the reason this can show up under breaking but not normally is that when you load the tire by applying the brakes, if the belt is bad it will squirm and "walk", effectively trying to turn the tire, thus pulling the car. This can be caused by either front tire, it wouldn't necessarily have to be the right side.
Also, if it started after replacing tires, you can pretty much be sure it's *not* a suspension issue.
Just out of curiousity, what the h e double hockey sticks kind of tires are these, anyways (brand and model, if you don't mind)?
Take care and enjoy the ride,