We have three little ones. I always say 'no ironing'. I don't buy anything that needs ironing. I'd always rather that our nanny pays attention to the children, rather than gets bogged down in things like ironing. And I like our nannies to take breaks while the kids are sleeping as it's totally exhausting paying attention to that many people during the working day. We have a cleaner to ensure that things stay reasonable and we don't ask our nannies to clean bedrooms or bathrooms. Just tidying/mopping up spills.
We do always ask our nannies to keep the kitchen pretty clean as they go. We use washable flannels (£2 for 10 from IKEA) for wiping up after meals and they're pretty robust, so it's child-table-highchair-floor in that order - all with one flannel, which then goes into a hot wash. Takes about a minute per child.
Having said the above, I would not like someone to start their working day in dirty clothes and I always notice and don't like it if someone does not wash their hands regularly or is not totally 'there' with hygiene. Not being able to cook at all is ridiculous and annoying.
The agency's T&C will absolve them from any responsibility regarding the nanny's suitability - this is always down to you. All they do is facilitate the introduction.
You may well have left it a bit late for the firing, in my view. If she was preggers when she started and has been with you for 5 months, she's not going to get another job now and therefore has nothing to lose by making things difficult if you fire her. So do be very careful.
Don't forget that your nanny is your employee and you do have a duty to be respectful and straight with her, even when she's really annoying you and not performing well in your view.
PS - no-one's cutting you any slack for the fact that you have triplets, which must be exhausting - physically and mentally, regardless of how much help you have. I do hope it all gets sorted for you.