[Richard]

I think you are on the right track to get fresh weights with trailer attached.

You have gotten some really good info from the members. You have pretty much covered the question of are the brakes working in good order.

To summarize what everyone has said, the problem probably lies in three conceptual areas.

One, the tag is not weighted properly causing the tire to skid before the drive wheels.

Two, the tag is braking harder than the drive.
Could be caused by something amiss in the relay valve for the drive or the pilot relay valve for the tag brakes.
Could be caused by the drive brake shoes not biting as hard as the tag shoes
Which could be glazed or worn brake shoes
Which could be that the brake cans for the tag are TOO big, could be a replacement or came from the factory that way

Three, the trailer is lifting the rear and unweighting the tag during a hard stop.
Does the skidding happen without the trailer?
Yes, you have stated the trailer has brakes, but we just don't know if they are as powerful as the coach brakes. The momentum of
the trailer and the effect of the weight distribution hitch want to raise the back of the coach during a hard stop. Might be an
interesting experiment to have someone video from a side view you stopping the coach. It wouldn't have to be a panic stop, just
moderate. Put it on the computer screen and see if the rear lifts.