Howard -- We stayed in Epernay (but in an Airbnb). The Airbnb did not have parking, but we found little trouble parking on the street. The town uses an app to let you pay for parking and it will send you a reminder when your time is up. My recollection is that the daily parking rate was about 9 Euros (but I was not in charge of payment). If you are driving to Reims or around the countryside then you have little need for parking in Epernay.
Because you will have a car, it is not really necessary to stay in Reims to see the champagne houses there. I would have liked to have seen Veuve Clicquot, but there was no availability when we were there. Their only public tour is not inexpensive, but you get to try some of their best champagnes. It seems that most of the houses that have multiple "tours" the physical tour is the same, the difference in cost being related to the cost of the champagne served after the tour. We enjoyed our tour of Taittinger (one of the middle ones), but were able to get a small taste of the Comte de Champagnes and ended up ordering six bottles. You should assume that each tour will be at least an hour and a half.
If you are looking for a place for dinner in Reims, I would recommend Le Millinaire. The menus are in French, but they are more that willing to explain each item. If you are looking for a nice dinner in Epernay, I would recommend Les Berceaux. We had lunch there shortly before we left and if you go I would highly recommend the pheasant soup for your entrée (starter).
Hautvillers is a relatively short drive from Epernay and a very picturesque town. In addition to the Abbey and the tomb of Dom Perignon, there are a number of tasting rooms for different champagnes located there.
I belong to several Napa/Sonoma wine clubs and have been to all of the champagne houses in the area except Domaine Chandon (owned by Moet et Chandon). Schramsberg's tour is the most similar to the type of tour you will get in Champagne. As far as I know Mumm Napa, Iron Horse and Domaine Carneros (owned by Taittinger) have only tasting areas. On the Avenue of Champagne you will get a bit of both, although some of the houses are not open to the public (Pol Roger).
There are hundreds of champagne producers, big and small, so you won't get to see them all on this trip. But there's no harm trying. :)
Chris