I feel bad for your big fella Milo - he is adorable! And it sounds like your neighbors are very self centered, considering they let their dog run free.
Telling the neighbor to leash their dog would probably feel great at the time. Someone suggested that and I thought "yeah!" But it sounds like they are enough problem already and it will just build up to one of those horrible neighbor stand-offs. So my advice is not to talk to them about anything until your kitty situation is settled.
Maybe for now just think about what will make Milo happy, since you can't control who will live next to you for the rest of his life.
My sister has 2 cats and her neighbor's cat drives her cats crazy. She does have a fence, and the cat comes under the fence, so I suggested she put aluminum foil and sticky tape near the openings and also talk to her neighbor about her cats being old and stressing out, and letting the neighbor know what she is doing. For now it is working.
With your Milo, maybe for now you could try supervising his outdoor time and going with him. Let him out for a shorter amount of time and be there with him. If he starts to go to the neighbor's yard, pick him up and bring him inside. Or pick him up and take him to the other side of the yard away from the neighbor and give him a treat. It sounds like he does want to sniff around and walk around a bit. If you lead the way with toys and string he may go along just for kicks, even if he doesn't care about your toys.
That is what we've done with our cats, even though it is an investment of our time. Over time the cats have substituted our attention with "outside" and now we do their play sessions indoors using the same toys (fishing pole with toy on it). Just having that time to play and have fun seems to do the trick and it gives them their fix for outside. But indeed when summer rolls around and especially if we are sitting outside, our Toby (same as your Milo) just howls and cries pitifully.
We can't let them out now because we have two ferals outside that we care for, and my indoor cats chase them when they are all outside.
In our old house, we had a fenced in back yard but our one girl kitty could easily get over it into the neighbor's yard. The neighbor complained and we told him to please do shoo and yell at her and scare her back to our yard without any water or violence. He was fine with taking that responsibility, so we had a truce. But it sounds like your neighbor expects you to manage it, and that is perfectly understandable even if she is rude about it.
Good luck. On the enclosure, you will probably need a building permit for anything you do, so that is something to consider. I am guessing the ban on dog kennels is to limit barking(?). I recently read an article about neighborhood associations and apparently they can be very powerful and scary. I hope that is not the case with yours. If I were you, I would visit your municipal building and become friends with all the people there informally. It sounds like you may need them.