I've had good results using 2 plungers on the shower before. Push down with a big plunger over the drain and hold it and then use a small sink sized one to pump over the overflow drain hole. Works better than Drano for me (I have a septic system so I have to avoid Drano anyway).
I cheated, I went to Home depot and got my own snake. I hate paying plumbers to come out, charge me too much and talk to me like I'm an idiot just because I'm female. If I hear one more service man call me Darlin', Sugar, or Honey, you folks will have to come visit me in prison. And I look horrid in orange!
ETA: Oh! and I HATE 'Little Lady!!!'
Can't happen, you're good people. Can you give the dog something to stop him up a bit? How about you lock him in the bathroom, that way, the plumber gets to smell it when he works in there tomorrow.
(Disclaimer: nothing against plumbers that may be members here, I'm sure you're good plumbers)