Hi All,
About 3 years ago, We had a drain added for a washing machine inside the house. It was added into the drain line for the sink/garbage disposal with a "y" valve. Recently, I noticed that water is backing up more and more into our sink and takes 10-15 minutes to drain. After doing some inspection and troubleshooting, it looks like the install is causing the problem. The "Y" joint with the washing machine is now sagging and there is quite a bit of build up due to improper drainage (3 years worth). I've tried a garden hose with pressure, using a pipe auger, and a few other methods under the house with no luck. My next inclination is to cut a section of the pipe out where the clog is, remove the clog, and add strapping, etc to let gravity correct the problem. Any advice appreciated. See attachments

Drain sharing kitchen sink and washing machine is a bad combination. Kitchen sink drain is the "dirtiest" drain in the house while washing machine empties lots of water in short period of time. Therefore, it needs clean pipe to absorb all the water.

I see from your photos that you have 3" common sewer pipe, which is a good start. But that sagging "Y" is definitely a problem. Cut it out and glue in new one. Re-establish slope and support that new "Y" with plumber's tape to prevent it from sagging again.

You will probably have to snake entire pipe as the blockage will most-likely be further down the pipe as well. Flush with lots of water. Also run lots of hot water through the pipe after the repair.

Hope that helps

Milo