I'm sorry today has been so tough. The meltdowns and rages are always harder to deal with after a period of calm and what you think is huge improvement. (((((hugs)))))
Please stop listening to the neighbors. Chances are that if they had a child like your son he would be so much worse than your son ever dreams of being. The child would not get the help he needs and would never know what to expect or think that anything he did was "good enough", just based on things you have said about the neighbors. The neighbor would let the child do what he wanted as long as the parents were not bothered - and if they were bothered then some real abuse would likely happen, largely because the tolerance of the neighbors is very very minimal. Heck, they are probably turning easy child kids into difficult children simply because they are lousy parents.
One way you can KNOW that you are NOT a lousy parent - AND YOU ARE NOT!!! - is that you worry about if you are. You also work, read, see docs, etc... to learn how to be a better parent. You are a super parent, a true Warrior Mom and it is time to put on your rhino skin armor!!
The rhino skin is a way to think of your "thin skin" that the kids and neighbors get under. I actually visualize the nasty things bouncing off of my skin when I realize things are getting to me.
If difficult child wants to call the cops, let him. Chance are he will be terribly stunned if you offer. Even more if you find the non-emergency number so that he CAN call in his next meltdown (I always thought it best to NOT teach them to call 911 during a rage, Know what I mean??). I even dialed all but the last digit of the child services number for Wiz on one occasion. I told him to think dang hard before he pressed that button because if he did call a social worker out to our home because he was so abused then he better be ready to leave when they get there. I told him I would NOT be held hostage by a child who thinks I cannot discipline him and if he thinks that then he can call and leave with them when they came to the house.
I also told him that he would be CHOOSING to NOT be part of my family, which means he would not have a mother, a father (big smile on his face here because I turned off his video game), AND he would NOT have grandparents, cousins, or any other relatives. I asked him if he truly wanted to spend the rest of his life with-o his dad and I and his sister and with-o Gmas and Gpas.
Talk about SHOCK!!! He figured that he would threaten it and I would freak and beg his forgiveness - NOT that I would give him permission to do it and explain that he was CHOOSING to not have us or his grandparents!!!!
Not sure if this will work with your difficult child, but it worked for us for quite a few years. Actually, all of my kids are well aware that they can report me to CPS anytime they want. But unless we truly HAVE been abusing them, tehy better be ready to leave. If we HAVE been abusing them we will go and get help starting the next day, but chores are NOT abuse and neither is schoolwork.
Having the cops come can be a HUGE eye opener for him. ESP if the cops reads him the riot act - and most will. We lived about 2 blocks from the police station when we lived in OH and I once took a raging Wiz there - he got mad as we were walking home from an errand. Boy did he stop on a DIME when an officer asked him exactly what he thought he was doing! It can be an awesome learning tool for our kids, esp if the cops can make them realize taht they are NOT going to get any help from them or most other adults. Heck, we called the police on Wiz when he was in 6th grade and the officer told us it is actually a law in OK that a parent has a DUTY to use corporal punishment on a misbehaving minor. Talk about shock - you should have seen husband and I, lol!