I have a slope in my backyard, about 6 feet deep and 30 feet long (more or less... I forget the exact measurements). It's overrun with mugwort and wild grass. I pulled it all up by hand last year and of course it came back in full force this year. I spoke with a neighbor who said he had a similar issue when he moved in, and after multiple attempts at controlling with manual weed pulling he caved and bought weed killer. He said it was a herbicide that inhibits photosynthesis. I haven't seen him recently to ask him the exact brand but I've been doing a lot of research on it and have come up with mostly confusion. Does anyone have any advise on the type or even brand I should use? Again, it's mostly mugwort and some sort of wild grass. I have dogs, too, so I'm apprehensive to use chemicals but being in CT ticks are bad, and this overrun area is only making it worse. The slope also has a TON of daffodils planted in it from the home's previous owners and I'd hate to do any harm to them. Frm what I can tell, most of the daffs leaves are gone now. Any advise would be greatly appreciated.

Thanks again to to everyone in advance!