CIS-2018 in Chisinau.

Thank you. Where can I find information on what is required to avoid problems at the border? I searched online but couldn't find anything.

You definitely need a pet passport and up-to-date vaccinations. And, I think, something else. Some kind of certificate specifically from a state veterinary clinic, in a specific format. Google it; this information is usually readily available, and cat owner forums often discuss it.

I can accommodate 3-4 people in Chisinau.

One minute you're in Korolev, the next you're in Chisinau. You're more like Figaro than Vigo!