Firstly aside from A2 nationals au pairs (hate the term) can work as much as you and they agree for appropriate pay. Therefore they are no more or less expensive than a live in unqualified inexperienced nanny, which really is what they are.
They shouldn't be left alone with young children because on general they have limited experience, no qualifucation and limited English which is a) potentially dangerous in an emergency and b) not great for your DCs linguistic development over long periods unless you specifically want a native speaker of a foreign language so your DC can learn it.
Au pairs can get OFSTED registered but it takes a long time, they need to do various courses in this country and a CRB will take a while to cone through.
Overall if you're planning to leave them with a toddler and a baby I would be happy with someone inexperienced, unqualified and far from home.
The good news is you seem to have space for a live in nanny which brings the cost down, many nannies are or are ready to become OFSTED registered and newly qualified nannies are often more affordable than people think.
How many hours do you think you'd need? And what's your childcare budget?
2 nights plus long day means you're going to be sleeping 2 of those days occasionally, so you need 3 days plus 2 nights of care which is a lot and I would say not attractive to an au pair (certainly it would cost more than the £75/25 hours standard). Plus factor in shift work and they won't be able to do English classes.
I think a 'cheap' nanny might be your best bet.