Get a flat bed and build a box at the front that is 3'X7'x3', divider in the middle, two doors facing outward. Us that for hogs and then go on top and put dog boxes that face toward the back of the trailer.
Then just pull the mule up to them from the back.
Build a ramp on the trailer and bolt tie down hooks in the floor where the Mule would usually be.
I would start with one of those car hauler type flat beds with no sides and build up from there. Put sides on it 3' or 4' high all the way around. The with the gate on back and boxes in the front it is cmpletley closed up.
If gates open up do dogs won't fly out... you could even put snaps facing the inside of the trailer and snap dogs where there is extra room and not have to worry losing any thing.
Sorry... I got lost in my own dream trailer.
Matt I am going to have to get you to build a bed for my MUle also.. still haven't got around to it. What is your going rate these days?