That is all fine and good if you want to tell her that about not paying half..
I am warning you though that it isn't going to do you a bit of good. She is going to think the same thoughts I am thinking...
Why is it ok for you to NOT want to clean the carpets and are willing to pay half? So it is ok to hire it when YOU don't want to do the work, but NOT ok when she wants to hire it done and you don't...
Ever heard of "win the battle but lose the war"?
That is where this is heading...
More than likely she will say to you..."Whatever, I just want to get it on the market. NOW. Fine. I will pay for it to be cleaned and I will have them in there asap."