I've had some battles with fencing over the years and discovered a few things that might be useful to you. I've had them tested by primitive sheep, horses, and for the last few years, a kid. A kid, who by 18 months had rendered the tight, 4ft high mesh fence I put around the back yard, completely useless. He could get up and over it in under a minute and there was no keeping him in. So...
Welded wire mesh fencing comes apart with very little abuse.
Wrapped wire fencing bends, scrunched, the squares slide and it becomes permanently scrunched and saggy regardless of gauge.
Hog/cattle panels hold up very well over the years. They do get climbed on, but handle weight well. We have some 20+ year old ones that even adults have stood on and they are still intact.
If you want to deter climbing a vertical metal fence would be a good option. Like this one:
http://m.homedepot.com/p/Mainstreet-Aluminum-Fence-3-4-in-x-1-5-ft-x-6-ft-Black-Aluminum-Fence-Puppy-Guard-Add-On-Panel-77331993/204187627?gclid=Cj0KEQjwioHIBRCes6nP56Ti1IsBEiQAxxb5G4ntNGdUmlg2T5kMAAhlULD1p_jwJHbqNUTQPugSCYUaAtYM8P8HAQ&gclsrc=aw.ds
There are also some supposedly indestructible pool fences that look sort of like big screens. Google "kid proof fence" and they take up pretty much the entirety of the results.
For living fences, I would think the cattle panels placed behind whatever you want to grow would work well. Not to trellis on, because kids will climb it and hurt the plants. Have you looked into Osage orange living fences?
You could also try planting bulbs a foot out from the fence on the apartment side. Kids pick flowers, but they seem to respect them enough to not step on them. Something like a mix of daffodils and tulips would have a long seasonal effect.
I've been working on the fence idea for a while too and I keep coming back to edible fencing. Blueberry bushes planted in a hedge...other large berry bushes...
Seasonally, you could grow hops and end up with a 40 ft wall of green. They smell nice too. Cattle panels would work for this with a simple wire above the fence line and hanging cords for trellis lines to get some extra height.
Another thought I've had with kids is to construct the outside of the fence in such a way that it is designed to be used. A simple bench along the length....actually making it to be climbed on. Handholds, busy board sections, short series of up and down steps, chalkboard paint inside thrift shop frames to make it into a gallery for the kids to draw on..... basically, if you make it to be used by kids, they dont want to use It! They'll play with it for a minute and then go stack rocks or something...Magic reverse psychology O.O
