@MommaGow, welcome to garden.org! You'll find lots of friendly and helpful people here!
Unfortunately, despite Sue
@sooby asking me if I can help, I can't even though I would like to. I don't know enough about the situation. And I have no experience battling stinging nettles in daylilies.
The only herbicide I am familiar with that will kill (some) broadleaf plants without harming daylilies is Lontrel. But it's not available in small quantities, not labeled for home garden use, and without looking up the label I don't even know if it will kill nettles.
Hand pulling with thick gloves and a sturdy long sleeved jacket such as denim or poplin might work if in fact they are shallow rooted. One site said they have rhizomes. Even if they do, continually removing new growth will eventually exhaust the nettle plants.
How large is the area? It might be most effective to dig out the daylilies after flowering, hold them in pots, and treat the bed repeatedly with herbicide until there are no new sprouts. Alternatively, put a light proof cover over the empty bed until the nettles are exhausted.
Sorry I can't offer any easy ideas. Maybe someone who has actually dealt with nettles will have something more encouraging to offer.
Pat