There are some simple things being overlooked. Plant roses and other thorny plants outside each and every window. Make sure windows can't be opened without breaking the glass...don't use bars because they could trap kids in a fire. Have good (and multiple) dead bolt locks on all the doors and make sure kids won't ever open for anyone but a family member or the cops--and then only if the car is marked and obviously the real deal.
If possible, re-arrange some of the family duties so adults are home more of the time.
YOU wrote that the kids are home schooled. If so, there would be an adult in there most of the time when others are working during daylight hours.
Get a meaner dog for outside, and keep at least one of the others inside at all times, preferably two--except when they must be let out.
I like the idea of making a safe room but expense could get in the way.
Can you put unrolled barb wire around the perimeter of the existing fence, just inside, so if someone jumps it they will get tangled up? There might be some liability in that, and I did once have a dog get hooked, but that is a nice (if not mean) and inexpensive way to protect a fenced yard from jumpers. I also like the idea of electrifying some of the fencing; or just hang the warning signs.