I don't know specifically about the Town and Country, but I would say that it's a good idea to get an aftermarket transmission cooler on any tow vehicle with an automatic transmission, regardless of whether or not it is "weak."
What is your vehicle rated to tow? There is some difference between towing a trailer that is close to your vehicle's rating vs. towing one that is, say, 1/4 of the rating. That's not to say you can't tow up to the rating, but just that the closer you get, the more I would recommend a transmission cooler.
Have you Googled about towing and your transmission? That might give you some good info from a wide sampling of people.
Not that you shouldn't trust the dealer, but over the years I've found that they are not always "up" on towing in terms of having the best information.
I have a real soft spot for the Compact Jr. I bet you're really going to enjoy it!