You know, I see exactly what you're saying, and I agree - it's not right. You paid Babies R Us for the protection plan, and they should make this right for you. Go to the store and speak with the manager. Often times, you will get a better result from a live person (who knows that s/he stands to gain or lose a great amount of money from you as a current and future customer), than from a customer service person on the phone.
Okay, stores won't take a RETURN on a breast pump, but you are not returning it. The store will return to Medela the broken pump, not put it back out on the shelf (they couldn't, it's broken!). So it's not a return, it's a warranty exchange. If the manager isn't seeing things your way, get the district manager involved. You paid the extra money for the protection plan through Babies R Us, their employee explained the terms to you, they should honor that, period. The way the person on the phone explained it to you means that you'll have to spend further time chasing down this $170, no doubt. I mean, what do you do if the check doesn't arrive within 10 weeks?! No thanks!! Raise hell with the manager on site at the store. Insist that this is resolved at the store level for you. Good luck!
ETA: Sweetie, I just read your SWH, and now I'm confused. You paid $170 for the pump, which is now broken. If they give you a new pump, they've made you whole. You don't get $340 PLUS a new pump. That doesn't make sense. Maybe I'm missing something? Seems to me that Babies R Us should simple exchange the broken one for a new one and call it good. Right??