What brand of laxative will work in 15 minutes-1 hr that isn’t too harsh? ?

You can't have both.

If you want results that quickly, use an enema instead of laxatives. Laxatives generally take 6-8 hours to produce bowel movement

Fast equals harsh, sorry.  Any laxative that stimulates the muscles in your colon to contract is going to work faster than one that increases fiber and water.  These stimulant laxatives are products like Dulcolax, Ex-lax, and Correctol.  You can ask a pharmacist or read the labels.

The problem with these products is that you can't guarantee they will stop as soon as you go.  Some people get "fecal incontinence."

Products that are less harsh are things like Miralax or Metamucil that increase fiber and water absorption in your bowels, but they take a few days to work and require you to drink a lot of water as well.  https://www.verywellhealth.com/stimulant-laxatives...

The only thing I can think of that will work that fast is vitamin C mineral ascorbates (sodium ascorbate, calcium ascorbate, magnesium ascorbate, etc., or mixtures of different mineral ascorbates), and it may be difficult to find locally. I guess places like Whole Foods or Vitamin Shoppe might have it. It's also called buffered vitamin C. Once you've taken the right dose (which can take a little time, as you usually don't take it all at once), it works pretty much immediately.

As for what is more likely to be available at a local store, I would go for magnesium citrate, but that might not work quickly.

If stuff is low down in your bowels so that it's close to coming out (just too dry to do so), you could use a fleet enema. That works immediately.

There's only one thing that will work in an hour or so! And there's nothing soft about it hot pepper juice! It'll go right through your digestive system and make you poop your brains out but it will burn every inch of the way.

Drink a bottle of prune juice. That should do it. Also drink lots of water every day.

     Suppositories.