You could throw your clothes directly in the washer and nanny can just throw the children’s stuff on top. I don’t mind the occasional pair of underpants, and like most in here I would be more inclined to help a single mother with laundry, but the dirty underwear and sheets are not ideal for me.

OP, first, I'm sorry for what you're going through. Second, I would just mention this when you interview a nanny. Some of the nannies who post on here would apparently refuse to do laundry at all, so I'd make sure to weed those out. Our nanny is super flexible about doing additional tasks as the years have gone on (she actually took our dog to the vet one day for us!). We've always asked her if she's willing to do anything outside the scope of her original position, but she's never said no. I wish you good luck with everything.

I agree with most of what other people have said. As long as the pay is fair and everything is laid out and discussed/agreed on beforehand, I see absolutely no problem with it. Most nannies are likely to be compassionate to your situation and would have no problem helping you out provided the conditions above were met.
Personally, I don’t get squicked out anymore at all by changing diapers or any of the various fluids children expel from their bodies on a daily basis. It just doesn’t bother me anymore. So I don’t think that doing someone’s laundry (underwear or no underwear) would bother me.
I’d be happy to help, especially considering the situation.

I’m a busy working mom with young DCs and a very supportive husband.

We got lucky with our long term Nanny.
We treat her well, pay her well, and she goes above and beyond every day to make our lives easier.

She’s grateful for long term and reliable employment so she’s flexible on the job describtion
I didn’t know to ask for someone who’d be flexible but it’s so value add. I think you’ll need it too as you’ll want someone to stay for years and be a reliable person in your DCs lives.

You can ask your nanny, and ask her references if she’s flexible and to give you examples.

Good luck OP!