I'd like to know what the hell Dr. Ya'll's dad meant by that bit after she went through the wormhole in "Contact in Space and Time"?

It was that everything Dr. Ya saw was portrayed by the aliens as she remembered it, which beach was the one she drew as a child, remember? That would make it easier to accept. And when "his dad" says "it's been like this for thousands of years", he means that contact with aliens can't be brought back to Earth with souvenirs or proof of anything, which means that there may have been Earthlings who've seen aliens before. And the transmission tool was not made by his father, but by the "people" on Vega, who have now left the planet. That's the way I understand it.