Put the pull-up back on until she is dry for a week. She's not sleeping, you're not sleeping, and you're up to your ears in laundry. Some kids just don't get this until later - it's not a defiance issue or anything else. The stage at which the brain gets the "bladder full so wake up" signal varies in every child - it's neurological and developmental, not behavioral. So you can't train them out of it. She's still pretty young so don't worry. My son was evaluated for this at 5, and there is a condition called "nocturnal enuresis" which means night time bedwetting. He had to go on medication until he was about 11 - it was no big deal, although I'm not usually a big advocate of meds when something else will work. When he was ready for sleepovers and later for overnight camp, this medication was a lifesaver. The pediatric urologist we met with said there were no side effects, and he even had kids in their late teens using it. I don't think you're anywhere near ready for this, but it's out there, just so you know.
When our son was little, we didn't have the good-nights diapers for big kids, so once he physically outgrew pull-ups, we were on our own. We tried those alarms, and they were horrible and unhelpful. You really don't want your daughter waking up 3 times a night to go to the bathroom - she needs her sleep more than she needs to be using the potty. I really think you need to look at the likelihood that she cannot be "trained" out of this. Limiting fluids will help her not be so drenched, but I wouldn't keep waking her or doing sheets!
If she tends to leak out of the pull-up, you can do what we did - put a waterproof mattress cover on, then a fitted sheet. Then we put a waterproof sheet (from the crib - it's just a flat piece, no fitted corners), then a 2nd fitted sheet. We kept a packet of wipes next to his bed. If he wet the bed, we only had to strip off his pjs and wipe him down, strip off the top sheet and the crib liner, and he had a fresh dry sheet ready. I've also heard people now use an absorbent pad available in drugstores with the adult diapers. You could try any of these methods if necessary.
Good luck!