We are having odd plumbing problems at our cottage. We have two bathrooms and every has worked fine the past year. About a month ago there was a major backup in the town sewer line that was cleared. Since then, we have had an issue where one toilet won't flush and the one that does, sucks the water from the other.

We've had the line snaked and the vent pipe checked. We have only one vent so our plumber installed a "cheater valve" and all was well until we had a very heavy rain this week. The original problem returned for about a day but now all is working fine again.

It doesn't seem like a vent problem as we did not have this problem in the past.

Any ideas what might be going on?

Did any or your neighbors experience any problems during the heavy rain? If so, I would suspect a city main issue.

We checked with the neighbor on one side and no issues. We did not ask the other one but they had a party yesterday and I think would have mentioned it if there was a problem.

the vent pipe checked

What does that mean?

our plumber installed a "cheater valve

Where did he install the cheater valve? Don't see how that could be done except on an existing vent line.

Are both toilet on the same level?

I don't see how this could be anything other than a venting issue.

Try this logic.
City sewer back up brings something solid into you sewer system. That blocks your sewer and vent. You clear blockage in sewer line but not vent. What ever is blocking vent dries out and vent is partially open or somehow one toilet is vented but the other is not. You have heavy rain. Water down the vent pipe wets whatever is in the vent pipe. It swells and blocks vent again. It dries out and toilet begins working again. In other words the cheater valve is not really doing any good.

Snake the vent from the roof.

Cheater valve is under the sink connected to the sink drain.

Plumber did not snake the vent pipe but did run water from a garden hose with no backup into the vent pipe - looked all clear.

With a lay out like shown below running water down the vent pipe would not confirm that venting to toilet is clear. Water would back up until it reaches the level of the kitchen vent and then flow down the sewer line.