"Overprotective"? How? She nearly left him at a park, let's him go off by himself as a teenager to spend a whole day hiking on Karlsson property, abandons him for who knows how long making him think she's dead, and then let's him be falsely accused, imprisoned for 2 months, and go through this brutal program? If that's "overprotective" I hate to see what Elena's "negligence" looks like in your mind. What was she "protecting" Kane from? Alexander? She's said herself that as long as she did exactly as Alexander wanted, Kane would live, so as long as she raised Olivia, and kept her hidden from Elena (and KG), Kane was safe, and therefore should have been safest after Alexander's death, but now he's in the most dangerous situation of his life, regardless of path.
There's a difference between a group of kids not wanting to play with your child, and the entire group bullying you, and this can be seen from afar. The absolute proof that something is wrong is the child not returning to mommy, but running off alone, so a present parent, regardless of what else is going on, is going to go find their child who ran off. The same applies for a child who storms off from his mother in a public place. Veronica, having a valuable piece of tech in a poor neighborhood, is in significant danger if alone by herself, not to mention the potential for kidnapping a rich girl for ransom, regardless if the kidnappers know if she's a Karlsson or not.