CNC is programming "for keeps". Any tiny little error in your gcode has a chance to crash the machine. Unlike a computer crash, a CNC crash results in broken metal flying across the room and anywhere from $5- to $5000 in damage. I programmed for a heavy machine shop for a year before I gave up and went back to making websites. Hobby CNC is fun though, it is amazing what you can make out of wood when you can shape it…
Using a Dremel tool as a CNC router never works very well. The motor isn't constant speed, slows way down under load, and can overheat. The bearings can't take side loads for long, either. It's been tried. A Bosch router from Home Depot works much better. Those can cut wood all day. You can take off the handles, leaving a motor cylinder that can easily be clamped. Also, enclose the electronics in something that will keep the dust out. If the stepper motors are not dust-tight, they also need dust protection.
You need dust removal. Any CNC router doing useful work generates sawdust in huge quantities, much more dust than hand woodworking. Absolute minimum is a Shop-Vac sucking dust from the cutting area.
Trying to make a machine tool from low-end 3D printer parts does not work very well. There are some far better open source CNC wood router designs. The Maslow project [1] is especially clever and very useful, since it can make furniture-sized wood parts on a low-cost machine.