okay, is the budget an issue? I think you said it was. Would you consider getting a live-in nanny and dropping the nursery? The money you save on nursery might make up the difference financially for you to move from pathetic au pair to responsible nanny. Of course moving to nanny does guarantee competance.
I realise you may have the toddler in nursery because it also functions as a place for early schooling/socialisation. It might be worth putting her name down on a few local nurseries just in case you might want to pull her our of full time nursery, get a nanny. And then nanny could take her to/from school as well as the other duties you have listed.
I think you could ask a nanny/au pair/whatever you want to call her all of the duties you listed (including ironing and definitely including swimming) if the kids are both off to school for a few hours a day.
I now have a live-in nanny who looks after my toddler from 7:00am until 7:00pm. I get dd up and she hangs out with me while I dress for work. Nanny takes over at 7:00, gives her breakfast, gets her dressed, and is responsible for her entire day. I arrange activities for them (Tumble Tots, swimming (Nanny is responsible for providing her own swim suit), etc.). DD is fed and back in her pyjamas when I arrive home at 7:00. Nanny also keeps the house tidy of DDs things, and does the whole family's laundary, including ironing. She does not put it away, though. She is not a cleaner and does not vacuum, dust, scrub floors, etc. But, she does keep the kitchen clean and this includes doing my dishes from the night before in the morning.
If I don't include the value of her room and board, I pay her less than I paid a childminder. If I do include the value of rent, it's about the same.
Like you, I require someone to get DD ready for her day, and keep the house in respectable order. I wouldn't trade it for the world. But, as you have obviously learned the hard way, as I did, a bad au pair / nanny can me a fantastic amount of work in terms of managing them. And, it is VERY difficult to manage someone whom you are not there to observe and supervise.