For god's sake no whisky!! Promise you won't!!
You need your mum to stay and help at night for a couple of days. It's what mum's are for.
As long as you are doing nothing - no driving, operating machinery etc that requires attention - try to roll with the lack of sleep. Even if you don't get dressed in the morning, so what? Eat, sleep, feed baby, cuddle baby, start all over again - it cannot last many more weeks. Been there, felt as deperate as you do, and trust me it passes. There are no really proven 'averages' that say what a baby should do. I never got a full nights sleep till they started school.
The only important markers are if your baby looks at faces, if s/he starts to smile after a month- 6 weeks, if crying is not constant monotone, and I'm sure if anything indicated problems your HV would be onto it. You're a tired mum with a toddler and a baby, if your mum can just let you get a couple of extra hours sleep you can cope with anything. Hugs.