So I'm assuming it's the night diapers that stink even when freshly out of the washer/dryer? Some ammonia is normal in a dirty toddler nighttime diaper but it shouldn't be so strong that it irritates skin or burns your eyes when removing the diaper. It also shouldn't hang around even after the diaper is clean. How long have you been using the diapers (and were they new when you bought them) and how long has the smell been occuring?
I'd definetly strip the diapers and reduce the amount of detergent you use. You don't mention how much you use and I'm not familiar with Tiny Bubbles but typically you shouldn't use more than about 1/4 - 1/2 (at the very very most) of the 'recomended' amount of detergent. You're already putting them through quite a lot of water during your regular wash routine (the whole routine is at least the equivalent of 3 cycles) so either you're using much too much detergent, the brand is particularly bad for build-up or perhaps you have hard water?
For stripping it's really up to you how you do it. You can just do plain hot water for each wash if you'd like (the hotter the water the better). There's no need to add anything else at all if you don't want to. I just mentioned the most common additives that some people use, but they're not strictly necessary. You can check at some point when there's hot/warm water in the machine and see if you still lots of suds, if so that's an indication that you should keep going as there's still lots of detergent in the fabric. You should know that it can easily take several full hot cycles to remove all detergent build-up, I know someone for whom it took 10 full cycles! Now, it doesn't always take that many but you shouldn't just assume that it's all done after a couple of cycles.
For the additives, if you chose to use them, you can basically add them any time, I'd probably put them in a hot wash just because most function better in hot water but other than that it doesn't really matter. Maybe just make sure you run at least one plain water cycle at the end just to make sure everything is rinsed out. The various additives could help whiten & brighten, remove odors, deep clean and perhaps disinfect. Vinegar can be interesting in terms of removing a heavy detergent build-up if used in large quantities and soaked in for a few hours. Liberally pour a few cups up to even a full bottle into your washer filled with water and diapers, let soak for a few hours. The acidity should help break up the detergent build-up (and mineral build-up if you have hard water) and speed up the stripping process.
Something else that just occured to me, if you have hard water that can also contribute to mineral and detergent build-up, many have had success using powdered water softeners like Calgon (either for stripping or in their regular laundry routine).
Rinsing nighttime diapers before putting them in the pail can be helpful as well, that's certainly worth trying I think. I would try to limit how often you go every 3 days as that's starting to stretch it out a bit. It's not a big thing but maybe worth trying since you're having smell issues.