Some campgrounds have size or weight restrictions, but many do not, including most public campgrounds. It is always wise, if you're not sure, to call ahead, but you shouldn't run into problems, so go ahead and get that RV and take your Bernards. They will love it. Of course, your Saints are small compared to the official record for the breed, 315 pounds!
As for towing a livestock trailer, I have seen many motorhomes pulling horse trailers, so the main thing you need to worry about (other than things like brakes, WDH, and other important safety issues) is the towing capacity of the RV relative to the weight of the trailer, including the livestock, feed and supplies when fully loaded. I don't know about campgrounds that allow livestock, except that some do have sites reserved for campers with horses. You might look into fairgrounds and other facilities that are often equipped for camping with livestock.
On editing, I thought I would mention that there are several websites (petswelcome.com, dogfriendly.com, and more) that will list pet-friendly campgrounds, and you can often find pet restrictions listed in campground guides. It is still wise, though, to call ahead to be sure. Good luck and we hope to see you and your Saints on the road.