I could never imagine locking my kid(s) in a room, especially at such a young age
Here we have a three strike rule like Grace and he will get a time out if he gets all three strikes. Then we do a 2 minute time out. Certain things are not tolerated at all, such as hitting, biting etc. Those are straight to time out. I always tell him why he's going to time out and after his time is up I remind him of why he was in time out. Then he apologizes and goes on to play.
But in your case they honestly could be acting up because they are getting so little sleep! Like you said they are whiny and fighting. I would just enforce naptime/bedtime. Establish a routine. You are their mom and they have to learn to listen to you. If they get up after you put them in bed, I would just continue putting them back to bed without saying a word to them (yes I watch Supernanny
Eventually they will get the hint and stay in bed. I recently went through something similar with Jayden (except he was taking extremely short naps, going to sleep late at night and waking up early) and within a week he was back to regular naps and normal sleeping hours. Your girls are 2 months older then my son and I would SOOOOO be ripping out my hair if he didn't nap!!
Our routine is like this:
8:00- 8:15 AM wake up
Change diaper/Brush teeth
9:00-12:30 relax/play/read etc/snack (somewhere around 10:30 to 11)
Then I will let him nap until he gets up (as long as it's been AT LEAST 1.5 hrs, if not I put him back into bed and tuck him in and tell him its not time to get up yet because he will still be cranky with anything less. He usually falls back to sleep) If he doesnt wake up by 4 I wake him up because if I don't he will not sleep at night.
4:00 relax/play/read etc/snack
afterwards relax/play/read etc
8:45 milk & storytime
9:15ish brush teeth/prayers/kisses/tuck him in
9:30 lights out
That's what works best for us.
As for the diapers, try the duct tape if you use sposies. Or maybe putting the diapers on backwards? I haven't gone through this yet but Jayden always has pant/shorts with a shirt on (or if its hot then just a onesie) at all times so he can't open his diaper
Sorry this is so long but I really hope it was some help to you. It must be so hard to be a mom of 3 LO's under 3!!