Your question is stability. Will the design turn over? You don't need any software for this, not even algebra. Only a ruler (ok, you could do this in CAD). What you need to do, is make a Free Body Diagram (FBD).
The FBD has:
- a center of gravity,
- several pivot points,
- a human messing with your design.
The center of gravity is where the weight of your design applies (red). The pivot points is the point around which your design would turn over, I think these would be the wheels of your design (pawns). The human is the force trying to turn over your design (blue).
The blue and red force cross at a certain point. That's where you can add them up. If you draw a triangle to the pivots from that point, and the resulting force stays within the triangle, it's stable.
Add up forces by putting them head-to-tail, starting from the crossing point. As you can see, here it's just unstable. But that's enough.
Now to make this work for you, you have to draw both the dimensions and forces scale. It doesn't matter how big the forces are in relation to the dimensions, just draw them in a practical size.
You can do this for slightly more complicated designs too! Here is an example of mine: a lifting crane with several weights, loads, working under an angle, and fully parametric.