Villa holidays with small kids can be lovely - we did them when our three were tiny. You do what you want when you want , you can give the kids food similar to what they have at home for at least some of the time, we found it easier to watch the pool area as it was private , not shared. Make sure you get one that is fenced with a locked gate - it really helps the stress levels!
But we always had at me and DH with us at a minimum, and sometimes my in-laws came too. We also had a car. Managing without one - especially for shopping - would be a real challenge.
Dont under estimate how difficult flying is with small children. Juggling buggies, car seats, kids , paperwork, and suitcases is hard work, and I’d say probably impossible with 1 adult. I don’t know if airports would give you assistance if you requested it in advance.
Also, remember that your kids may struggle with a change of routine/food/heat etc. Mine were great kids at home, but could be hell on earth for the first couple of days on holiday, until they settled.
if you think you can manage all this on your own, then go for it. But having done it with more than one adult (and it being hard work at times even then), I wouldn’t even consider it. I used to take regular hotel breaks to London on my own with three small kids, so I was used to doing some travel in my own with them, but two weeks abroad would be a step too far.