Alternatively, weld the vertices when you export.
When you subdivide a model the smoothing algorithm causes the surface to contract. When this happens at the edge of an object, the edge pulls in – especially at the corners. That’s exactly what you’re seeing in your screenshots. Those areas where you’re having the problem are places where points from two separate surfaces overlap. So when you divide the mesh, they pull apart.
There are actually three methods you can use to prevent this, depending on the needs of your model:
Welding will merge overlapping points.
Edge loops will add extra geometry that hides the contraction around the edges. (It still happens, but you don’t notice it because edge polygons are really thin to begin with.)
Tool>Geometry>Crease will also prevent the edges from contracting. Apply that before you divide.