When toilet is flushed, water and grey water comes up into the tub. I understand the roof vent pipe needs snaking, but can drain cleaner or power washer be put in the roof vent pipe also?
Debbie

Hi DJ, I personally don't like to use chemical, why not just snake the drain?

I agree with Parttime. As a repair plumber I have never recommended using harsh chemicals. In your drainage system. Besides they only seem to work in TV commercials and when you try to remove the water you could burn your hands or damage your eyes.
If you usem a power washer in the roof vent expect to see a explosion of dirty water erupt from your lavatory and bathtub as soon as the pressure hits the blockage since water always follows the path of least resistance.
Snake the vent! **OR**
Since the clog's downstream from the tub you could snake from the tub overflow ,(see image)
Unscrew and remove the overflow plate,(The one with the drain lever) and pull out the tub stopper. You now have a clear shot at the trap. The way you were going in through the drain it ran you square into a tee that you can't get around. Now feed the cable( 1/4" best or 3/3" with a small tip. You can rent a Ridgid K50 sink cable.) About 2' down you will run into the bend of the trap. Crank and push at the same time to work around it. Your blockage will be found in the lateral pipe going to the stack. You shouldn't have to put out more then 10 or 12 feet. I have found tub and shower clogs to be mostly hair and the worm should auger into it and pull it back. After you snake pour a few pans of boiling water down the drain. This will loosen the grease and flush the mess out into the main. Hope this helps and thank you for rating my reply. TOM