I need dog training advice, please.

[TsPoet]

Some really good ideas. Here is my take (without actually seeing your dog.)

Last (and this is a bit gross) you can take a match (paper, not stick) & insert it slightly into the rectum to get the poop action going. People who show dogs in obedience do it because if they poo in the ring, it's an automatic disqualification. Bring rubber gloves.

I show my Italian Greyhound, I do performance events with her and my 2 mutts and I have never seen or heard of anything like this. In the circles I know of, this would never ever been done/suggested. You could damage your dog's rectum, and the likelihood of it fully working is dubious.
I am off at dog shows about 2 weekends/month - so been to lots of shows/trials...
(almost every trial I've ever been to, at least one dog poos in the ring - it is an NQ and talked about, but not the end of the world and not a DQ - which is much much worse)

[Dogmama]

It is done quite gently with the paper end - and only inserted about 1/2 inch. It works by stimulating peristalsis.