OMGosh....That's so sad ....bless her heart...
I would let her inside ...maybe set her up in the kitchen ? but let her be near you if you can....She shouldn't be outside alone....the smell may be bad but she may not understand why she's outside....and you want her to be as comfortable as possible....
but it sure sounds like that time ....and I'm so so sorry....
that same thing happened with my husbands cocker spaniel Princess....we made her a nice bed on her last day and spent time with her before going in....but it's so so hard to do this and I don't envy you at all....I hope she isn't in pain but it sounds like she is and that's just heartbreaking...
My heart goes out to you and Flossie and you need to be strong for her...I'm very sorry.