Let's see if I can clarify any of this.
If you do not have a Ky cdwl, you can't carry within 1000 ft of any k-12 school property.
If you do get your Ky cdwl, then federal law will not apply to you in Ky, however, you still must follow state law, which says no carry in school buildings, buses, etc., or on school grounds, unless your firearm remains in your vehicle, and if you leave the vehicle it must get locked. This means you can carry within 1000 feet of the k-12 school property, but you can't cross the property line.
The k-12 school law in Ky does not apply to say a McDonalds, if a k-12 school function is
going on. It only applies to property owned and operated by the school district. The lousiville zoo tried banning firearms because k-12 schools used their facility. The zoo is not owned by the school district, they saw the light, and are no longer prohibiting carry.
This law has nothing to do with post-secondary institutions. These institutions however was given the authority to prohibit deadly weapons on their property in the 96 concealed carry law, (unconstitutional I might add). This means it is not against the law to carry there, but if your a student they can prohibit you from ever entering the building again,
and ruin your education. Hopefully this unconstitutional crap will be gone soon.
"no firearm" signs do not hold force of law in Ky, and they can be ignored. If someone who owns or manages the property asks you to leave, then you must leave or face arrest for trespassing. If a place is off limits and is stated off limits in 237.110, it is against the law to carry there regardless if it's posted or not. This would be places like "k-12 schools, and court of justice courthouses.". Don't forget, most of the places listed in 237.110 are off limits while carrying concealed, but not while carrying openly.
I strongly suggest reading krs chapters 237, 527, and 503. Check past attorney general opinions, and supreme court cases, the most important being "Holland vs. Commonwealth"