Yes and no. Some brokers co-broker on
DVC resales; others do not.
However, I don't think you could get another broker to take over THIS offer at this point. It that's REALLY the contract you want, you could rescind your current offer and make a new offer through another broker. If you decide to do that, I would be sure the new broker understands all the specifics of your first attempt so that a conflict between brokers doesn't mess you all up.
If you mentioned the broker, I missed it, but from the difficulties you're having I'm guessing you're dealing with Fidelity. Frankly, I'd just go to another broker (or more than one), tell them what you are looking for and how much you want to pay and go from there.
There is no shortage of resale inventory out there and not much is selling. In a buyer's market, I see no reason to cling to one contrract or one broker who's not responsive.