Nanny trouble

You can't reasonably expect a nanny to jump straight in and do your role as well as you do it. In time I would expect a nanny to be able to do everything you list but in the first week unlikely.

How long has she been with you? Did you go through your daily routines/jobs at handover?

Agree with writing out list.
Have to do this for AP.

First thing I'd do is find out if she'd had a terrible day. If the twins didn't sleep for some reason, and needed to be entertained or comforted it's quite understandable that she got behind with all the household duties.

I know exactly why you're annoyed - because you're having to clear up after your nanny when you come home exhausted from work. I think they're standard jobs so it's not surprising you're ticked off. You're using strong emotive language like "lazy", but don't get annoyed, at least not yet, until you talk to her. Take it from me as a many-times employer: being annoyed when starting a conversation with your nanny is not going to be helpful in getting what you want. Talk to her calmly, friendily and assertively, just focus on the tasks that need to be done and don't make comments about her capability or personality. See if it improves in the next 2 weeks.

Ok of the above things, the lunchbox, sweeping the floor and the nappies are things I probably wouldn't do until after the children have gone to bed. The toys she should have got the preschooler to help tidy at the end of the day. The crumbs on the surfaces she should have wiped down. You say your twins have 2 long naps during the day, but maybe things all kicked off once the preschoolers got home and that's when the mess was made. I wouldn't be too uptight about the cleaning if she's great with the kids, unless she continually leaves the worktops in a mess.

List jobs to be done.
Create procedures if necessary such as a routine for dealing with the reusable nappies, such as what needs to be done daily and what can be soaked and done every other day or whatever your procedure is.

Does she know how to use the tumble? What quanity it will take. Are there other ways of drying clothes such as a rack/airer?

Pick up on things now so that they don't become a major issue. Perhaps a task got abandoned mid way through.

It's stuff that should be done, but I wouldn't be annoyed yet. It's a lot to take on and she's probably still settling in, getting into a routine etc. Remember everything takes longer when you don't know where things are and how things work. I would have a gentle word and see if things improve. As she becomes familiar with the children, the routine and the house everything will become quicker and easier and I would expect that stuff to be done.

I think some nannies just need a bit more organising than others until they get into a routine. Sometimes you need to be quite prescriptive
Leave a list for tomorrow -

1. Please put on a load of washing, take out of dryer and put away
2. Please can you put some nappies on to soak and wash and put away
3. Can you empty out ds' lunch box and wash and put away
4. Could you please wipe the surfaces after dinner

Mention that you've left a note too in a friendly way.

Everything you've mentioned is standard nanny stuff.

What have u put in a contract with her?
Ask her why nappies not cleaned.
Make it clear 2 her what u expect her 2 do.
Dirty nappies r unacceptable - very unhygienic.
Would give her 1 more chance then warn her that she will lose her job.
Seems unaware of hygienic practices.
Not a nanny in my view, more a babysitter.
Is this her first job?

How long has she been with you? Is it possible she had a crummy day, twins missing you, eldest being defiant, feeling a bit under the weather herself?
Or is this typical from her? I wouldn't hesitate to point out she needs to keep things tidier and keep in top of laundry.
I'd be friendly about it first time I said something and see if it improves.