Ah, I think I have the same type of setup. I have a very large window at the back of the rig. But at the bottom there are two short, wide windows that crank open. Both window openings have frames that hold screen material in place. Is this what you are talking about? On my rig the screens are about 10" x 34" and have radius corners on the bottom outside corners. If so, then that would have had to be a big dog to reach that high or you might want to stop taking the dog for a walk inside the rig.
Other than contacting a dealer's parts counter to find a replacement (cha-ching!!!), maybe an internet search can locate a vendor. You'll need the exact dimension of the frame. I've seen replacement windows, but just the frame that holds the screen is probably a tougher search. Like was mentioned earlier if you can provide the model number of the 2009 Mountaineer it might be easier to provide what's needed and where to get it.
You might also be able to find an RV parts surplus supply store. I believe just about every picture window of this size uses the same size screens so their availability should cross all brands. Hopefully, someone can provide a source or name or link to make this search easier.
Please post your solution to pass it along! Thanks!