Hi Lextiger - not sure how much computer power your mother needs, but might help us w/ more specific suggestions; Lisa provided an excellent solution; of course, another would be to purchase an Apple laptop - a larger Macbook Pro would likely be satisfactory (and portable, if needed).
The only other thought (i.e. other than buying some new furniture - ), would be to explore whether 'wall mounts' are available for the newest iMacs (see these Amazon Offerings - which appear to be for older iMac models) - you might want to go to Apple online and do a 'live chat' to even see if an iMac can be ordered that would adapt to a wall mount. NOW, being an amateur woodworker & home DIY, I bet that it would be a real PAIN trying to install such a mount w/i a small cabinet.
Let us know if you need more specific advice - Dave
Put an eye hook in the back of the cabinet, put the iMac in the hole pushed backed as far as it will go and use a zip tie to keep it in place. Might cost you a dollar. I'm guessing the screen would sit between 1/2" to 1" in front of the face of the cabinet.