I picked up an IRD cartridge bottom bracket and their Swiss thread cups to use on my low end Batavus project. Supposedly you're supposed to be able to just pull the English thread cups off and swap them. The non-drive side was a little stubborn but I was able to pull it off by hand. The drive side is a different story with the cup not wanting to budge at all. Looking for any ideas to get it off. I really don't want to tear it up that much trying to get it off.

I'm not up to date on your project, but are you saying the Batavus has a Swiss thread shell with a British BB in it right now? That's understandable, but I'm a little confused as to why a Dutch bike would have a Swiss thread BB shell.
Swiss thread is a little larger diameter than British, and a different pitch. They are not interchangeable. But the smaller diameter British thread can be forced into a Swiss thread shell. Shouldn't be, but often is when you have to made do, because of the rarity of Swiss thread BBs.

No offense intended, but I'm assuming you understand that both British and Swiss thread BBs have a LH thread on the drive side cup, and it removes righty-loosey (turning clockwise.)

If you're turning it the right direction, I would suggest some heating up of the BB shell with a heat gun or even a blow dryer. Not enough to burn the paint, but enough to make it uncomfortable to touch. That usually helps unless the BB cups are aluminum.

You are misunderstanding the problem. The OP wants to swap cups on the cartridge BB. I'm not familiar with the IRD BB, but you can switch cups on a Campy.

Oh right. I get it. Sorry!

The DS cup is probably interference fit. That being the case, heat it up a bit, thread it into the BB shell a few threads, and give it a good tap with a hammer. Should pop right out.

Correct - it took me awhile to figure out the threading was Swiss. I originally tried an English threaded cartridge bb that I had on hand with plastic cups and they wouldn't thread in all the way.

The original bb had a cottered crank and spindle but the crank was nasty so it went to the dump. I tried a couple of different spindles with the original cups but they seem to be thin wall like a few of my old French thread have been so there was still too much play in the spindle when the cups were seated all the way. That's when I decided to move to the new IRD cartridge bb - which probably is overkill on this frame.