This all started about three weeks ago. I had been using flushable kitty litter in the toilet in bathroom one (older one). I had had some back up in toilet two (newer one) and used the plunger to clear it up. It did look like particles of kitty litter were being sucked in and out of the toilet when I plunged.
I have had mysterious air poppings in the laundry sink near the kitchen and toilet two for the last week or so. Then the shower had standing water and toilet two was slow to flush. I started using an enzymatic product to flush out the pipes in the laundry sink (which was the first drain to pop a few weeks ago) as well as kitchen sink, bathtub, stall shower and both toilets in rotation, not all at once.
This morning I noticed that toilet two was popping in response to me shutting the sink faucet on and off to brush my teeth, then wash my face, etc. What do I need to do?

It sounds like you need to have your drains professionally cleaned. Maybe even jetted. Never flush anything other than human waste and the minimum amount of toilet paper required. There are a lot of products that say they are flushable. Don't believe it.

I fully agree with CHayn. Time to have the main drain augered. There really isn't any true flushable kitty litter, flushable tampons, flushable moist wipes, paper towels etc, etc. Well, I guess they are, flushable, because they do go down, but they are not as dissolveable as say, toilet paper. Putting ANYTHING other than human excrement and tiolet tissue down a tiolet will almost always eventually cause drainage issues.

Final thought. Have the drain cleared, and don't put any more litter in the $hitter.