TBH, I would be tempted to take the fastest on the camera but have the longer of the pair in a pocket. If possible, get rubber hoods for both - as said above, press the front of the hood against the glass (and hold it there) and use the flex when aiming/composing. I use this method when shooting through glass whenever possible and it cuts out more reflections than even a polariser can (although some reflections do creep past when shooting through double glazing). IF light levels are high, a polariser can help but that will cut the light considerably - not ideal in that situation.
Not sure what the max useable ISO is on the D7100 - I would think you should get away with 800 at least - have a play and see what You're happy with WRT noise etc. Don't be tempted to flout the no flash rule - at best, you're likely to get thrown out and at worst, it could potentially lead to a complete ban on photography there. If you can't get any decent pix of your own, buy a few postcards!