There does need to be someone with a gun I can call if someone is literally breaking into my home intent on murdering my family

well-funded social workers and emergency first responders who are trained to resolve conflicts while actually helping those in need of it without threat of eminent deadly violence.

If we do things properly, then no one should have a need to break in to your house (because everyone's material needs would be met), and if you've given someone reason to kill you, calling someone with a gun to kill them isn't going to solve anything. If they're mentally unwell, calling a person with a gun is even worse.

The second option you gave is more than enough 99.99% of the time.

Some degree of community defence might be imperative, but it should never be one person with one gun who is in charge of "enforcement", but everyone would be trained and everyone would have access, and in a time of real need (like an external and violent threat to the community) those ready and available can do what is needed, but again - killing someone isn't it 99.99% of the time.