Agree with BigAl -- I have a 6x12 UDump I use for the same purpose as you. I don't even have to worry about a backhoe on my TC18, but I always have something else back there, usually a box blade when I'm messing with dirt. You should be able to mount a ball somewhere on your bucket so you can pick up the trailer and move it. If nothing else, weld a receiver on the top of the bucket, sticking straight up like a unicorn horn, then curl the bucket down so the receiver is horizontal and stick in the hitch ball.
I drive forward with the trailer on the front and simply push the trailer backwards. My son-in-law laughs that I should put a wired remote on the dump switch, then I wouldn't even have to get off the tractor to dump (as long as I move around with the dump door open).
I actually haven't welded a receiver on my bucket yet; I just pick up the trailer tongue with the bucket and push it. It slides around a little, but that hasn't caused me any problems, yet. If I do have to pull the trailer a little, I get down and hook the traiiler's safety chains to the hooks on top of my bucket. I'll weld the receiver on the bucket when I get a round tuit...ahould make a good base for a gin pole, too.