First off - a classical nylon string guitar *is* an acoustic guitar, just like a steel string acoustic is. The latter is also called flat top or western guitar.
An definitely no, you don't want a classical guitar in your case - these guitars are in fact harder to play although the strings themselves are softer. This has to do with the wider fretboard, the increased string height (action), and the longer scale. The scale makes the distance between the frets larger. In sum, they are harder to play - in particular for someone who might have less reach.
I would definitely try and get a good steel string which have been properly set up with light strings. Any guitar which haven't been adjusted properly is much harder to play!
Also, you might want to check out a 3/4 guitar. These are smaller than the full size ones. Just make sure you get a quality instrument, like a Baby Taylor or a Little Martin, Most 3/4 guitars are children's toys.
If you opt for a full size, do check out various box sizes. The larger Jumbo and Dreadnought models are more challenging to reach around for a smaller person.
Another thing you might want to try, perhaps if everything fails, is to use an open tuning, like a D or G and play around with that - there's a lot of fun you can do on a guitar without going for hard to play barre chords :-)