@middleager - I still shudder too, and they are 9 now!
I recently saw a woman walking around the supermarket with baby twins lying in the trolley seats (the ones that tip back for young babies). I had to go into another aisle because I felt so sorry for her and started to well up.
I already had two older children and had been quite a confident mother, hadn’t struggled with the newborn phases, or the jump from one to two.
I used to go to a twins club. There was always at least one woman crying. Twins nearly broke me.
My parents had looked after my single children sometimes, quite happily. But after having the baby twins once, my DM said to me, quite simply “We can’t have them both together again, it’s too hard”. She said that her and DF were “shell shocked” 
OP, I’ve missed how nearby you live, why don’t you offer to help out by having the twins for a couple of hours to give them a break? Better still, try 24 hours. Then come back and talk to us about it.
Or even take just one twin? Your sister and her DP will find even that an absolute walk in the park, after having two relentlessly.