Thanks a lot for your ideas.
Playing on the dining room table is a way to keep them in the same room but safe. If I send DS1 to his room he will feel jealous and lonely, and I cannot leave DS2 unattended (he is still 11 months old).
This leads me to the following question. If your older son/daughter is playing in his bedroom, how do you avoid that the little one goes in there? Do you just close the door? Don't you have any kind of a drama there? My little one always wants to be with his brother, and now he only crawls...
In any case I see that playing in different rooms will be necessary because everything that my DS1 constructs, my DS2 destructs, and it is getting more and more difficult to prevent it. May be I am over thinking it too much.