RG11 is four-pin (two pairs) phone cable, so you are getting some form of DSL service with TV on top of it. The box your ISP has provided takes care to "split" these signals onto coax (TV), RJ11 (phone) and RJ45 (Ethernet).
So, think about moving the "other" side of that box (coax cable, and Ethernet cable) to that "other" building. Not an easy task if you have to cross an open space, or more than 300 feet.