I’m having a hard time figuring out what’s going on in your model. But- I think- any normally stable piece of furniture is going to have a tipover axis formed by the points along its forwardmost edge- the front two legs of a chair, the leading edge of a bookcase, and so on. You have a considerably more complicated shape than either of those, but the principle still applies. You just need to calculate the tipover moment on a plane perpendicular to that axis.
All that said, I would just simulate it in Solidworks Motion or print out a quick 3D part. Trying to calculate this stuff is more trouble than it’s likely worth.