How old is the dog? I wonder if this dog is showing how unhappy she is in this new situation. Has the owner come to visit her??
(When my friend moved, he took his 1 yr old dog with him. The dog went from a big backyard to run free all day to a small 10x10 bedroom for 8 hours a day. The dog was NOT happy, and showed his owner so by pooping and peeing everywhere in that 10x10 bedroom. He was house-trained fine, but was not happy being so confined and this was his only way to show his owner his unhappiness. I ended up getting to keep the dog as my own and I am so happy. My dog turned 11 just a few weeks ago). But consider it -- that this dog just misses her owner and is acting out accordingly.
So what would I do? Call your friend, tell her it's been a month, ask if she has another friend who could house sit for a month and possibly you could take the dog for the 3rd month ...... Or tell your friend about the poop and the cleanliness of your house and the health of your kiddos. I dunno, you may have to exaggerate the problem to get her attention.