If I were you, I would cross post this on the Home Repair forum. It may be something in the underlayment or something else entirely. But it sounds like whatever is causing it, you need to pick up the laminate flooring in that corner. They can tell you how to do it. Here is a link that might be useful: Home Repair Forum

I am not a plumber, but I think I know what is happening. The "cap" is a vent to prevent a vacuum forming in the sink drain. It is spring-loaded and, without water flowing in the drain, does not allow air into the drain nor allow foul gasses out. My guess is the short horizontal run of pipe from the "T" to the vent is clogged. When the shower is running, the drain water forms a vacuum in the waste drain system. This vacuum pulls water out of the sink trap allowing the foul gasses to escape through the trap and sink drain. An unclogged vent would have opened and "killed" the vacuum. I believe your sink drain is improperly plumbed as far as venting. I suspect you have the infamous "S" trap rather than the desirable "P" trap and also have a problem with the bath drain venting

Get one of the 'zip removers' from the big box store. They are designed to remove hair from the drain. Any number of the Chinese made pop-up drain sets do not have a method to remover the pop-up without taking the lever under the sink out that moves the pop-up. Hair, especially longer hair, catches in the drain mechanism above the trap and then collects soap and other debris. The small can also be from the overflow path built into bathroom sinks. Debris in the path can start to smell. Hot water with some Clorox, and possibly even a small long bottle brush can often clean the overflow.

clogged vent maybe. if it is clogged the trap will empty and let the gases vet into the house. pour about a half cup or so of water in each and do not use them for an hour. if the smell is gone, then the problem is the vents. usually you can see the vents coming out the roof directly above the fixture, so you just go up and remove the birds nest or insects cloggin it. some cases it won't be that simple and you may have to get a pro in to clear them. also, if the plumbing is real old it may just have gunk built up that smells. you should be able to look into the drain and see it if it does. get a flexible brush like for cleaning baby bottles and use it to clean the drains down to the trap.