With little kids, and older, you don't ask then walk away. You ask & stand there doing nothing else but waiting for them to get it done, until it's done. Sometimes this is required with older ones, too.
If they say "in a minute" then you ask them for a commitment of when is "in a minute". And you are back in the vicinity within 30 seconds of that time they chose to see the matter is done. Waiting like a bad smell until it's done. Then you say thanks & move off. They like this consistency.
You say she 'refuses' but do you just mean she refuses repeatedly until it gets done? Then it still gets done, you just need to stream line the process. Try very hard to take your emotions out of the interaction. These are just chores, tasks to be done. You being emotional doesn't make a chore easier.
Tidy room: is it actually a health hazard that will attract vermin? Otherwise, this is not a battle I would pick.
Walking the dog: it wasn't really her choice to get the dog. Even if she begged originally, you're the responsible adult. Would be nice if she helps, but the dog's needs are your responsibility. I would remove this battle zone.
Sounds like you both resent each other right now.
Listen to everything she says that is not actually abuse, btw. Be the person she knows will listen to whatever is in her head when she needs to share. This policy will help re-establish better comms between both of you.