Your itinerary actually looks pretty good. It isn’t too rushed. Should be a lot of fun. My thoughts:
 
Take at least one day off of Barcelona (if not two) and add one or two of those to Berlin. Berlin is an awsome city worth spending more than 2 days in. If you take two days off of Barcelona spend one more in Rome or add a smaller place you could visit.
 
Financially it sounds doable. You also might consider going to a couple of little villages along the way instead of all “big” cities.

I stayed in Menton last September whilst on a rally.  We had a very wicked night there.  Good choice.
If you need somwhere to stay, try the Etap hotel (google them), its a bit of a walk along the promenade to the centre but who cares about that because the hotel is only €35 per night per room and each room sleeps three.
In fact the hotel is under a kilometre from Italy.

We actually have booked a hotel in Menton.  I believe it is called Hotel Moderne.  It might be worth it to check out that other hotel and cancel these reservaions.  Any ideas from anyone on daytrips/fun sites to see in any of these places?

Your trip looks well planned.  They only change I would make is putting another day or two in Munich by taking away from amsterdam/corfu.  Reason being is that area is PACKED with great places to visit.  The Alps are a must see.  Munich itself is a great city to spend a few days in.  Plus there is garmish and in 45 minutes you can be in austria.  As I said before there is a lot to see in this area that could/should be done all in one trip.