We own a house in Washington State that we have been renting on a Month-to-Month basis. The tenant gave us notice that she would vacate on April 12th and paid rent only through that date. On April 15th, we inspected the premises and the house was full of her belongings and filthy. We contacted the tenant to see what her plan was and she had already moved out of the country, leaving behind arrangements for her representatives to finsh moving her stuff out and cleaning it. Her representatives failed to do so on the original timeline she worked out with them. In all, her belongings were not removed and the cleaning was not comlplete until April 21st. Is she responsible for paying rent for those nine days where her representatives were traipsing through the house, preventing us from re-renting it?

Yes. Did she hand over the keys to you? Or did her reps do so on the 21st? While it probably doesn't matter that could cinch the issue.

You can deduct the unpaid rent from the security deposit as well as any above normal cleaning you needed to do. Document everything!

If the costs exceed the deposit you will have to file suit for the balance.

BTW, if a person is on a month to month basis, generally the notice requirement is one full rental period. So she could be held responsible for the whole month of April. However, if you agreed to a prorated amount, that would take precedence.