In reality, any plunge router is capable of this. The most important thing though is controlling it (and the workpiece of course)
Assuming that your doors are not moving, the router is the issue.
By the pics, I see you are using the edge-guide, which is good.....for one direction. It won't allow the router to move inward, which is only one direction. You still need to deal with the others.
Do you have an FS (Guide rail)? This can constrain the router in every direction, with proper clamping, of course. An MFT, or other dog-hole table top, can be very helpful in that regard.
If not, since you are saying that it seems to be going the same direction, clamping a block to the work surface might help. The edge-guide is resting against the door at a specific point, when the bit is lined-up with the right point. "Stop" it at that point and try it again. This may work, or may force the movement another direction.....test on some scrap.