If the LiquidPlumber solves the drainage problem for a few weeks than the vent stack isn’t probably what’s responsible for it. I would start from looking for a clog in a pup-up drain assembly, p-trap pipe beneath the sink or in a short, horizontal pipe section that runs from the p-trap into the wall... of course you may have a different setup, and you’d need to take it apart.
As for the clothes washer, I don’t see how the condition you’re describing could be related to a clogged vent stack
. I have recently replaced mine top loading washer with a front loader. The old one was serviced a couple of times by the Sears technician.
One of the reasons for servicing was leakage from underneath which happened only while using the “full load” setting. I don’t remember the brand of this machine but our technician mentioned that some of the top loading washers have a problem with top rim seal which tends to leak water when fully loaded and especially during the spin cycle.
The only solution he recommended was not to use that setting
or complain to the manufacturer.
Let me know if you have more questions, just click "comment" below.