I believe the "no gun outside the home itself" part will be struck down. The 2nd. A. states:"....., the right of the people to keep AND BEAR arms, shall not be infringed." It's one right. The word AND makes them inseparable, or at least it should. Thus, if you have the protection of the 2nd A. as a fundamental, individual right to keep arms, and the states and localities are bound, then you can also BEAR arms as that is part of the fundamental, individual, right as well.
The 2nd doesn't protect just the right to keep arms. It protects one right, which is composed of the actions of keeping AND bearing arms. It will be very hard for any government entity to wriggle out of that constraint. Not impossible, but it should be very hard if our courts hold true to the Bill of Rights. That has certainly been a problem in the past. I'm under no illusions that it will be a slam dunk with our modern courts.
"If you love wealth better than liberty, the tranquility of servitude better than the animating contest of freedom, go home from us in peace. We ask not your counsels or arms. Crouch down and lick the hands which feed you. May your chains set lightly upon you and may posterity forget that ye were our countrymen." Samuel Adams.