We travel (see signature) with three cats. I would think that with three dogs, you'll want a minimum of 21' in TT size, probably, even better in your case, 24'. While there are some that can get by with less, for your comfort and the dogs, adequate space on those days where the weather may force everyone to stay inside, 21 or 24' with a slide would give you enough space so that you could get around inside without having your mate or a dog always underfoot. Dogs like space to move, more so than cats, and IMHO, 24' would be as small as I would go with three dogs. That's our experience at any rate...
My 2 cents, your mileage may vary...
2 Cats; J-Lo and Ragamuffin :R
2014 Thor Tuscany 40RX DP
2011 Ram 2500 Longhorn CTD HO
2011 Keystone Cougar 318SAB (now gone)
2008 FunFinder X 210WBS (Sadly gone)