My parents have lived next door for two years. Am I in the wrong to feel so angry at them for their behavior?

2 years ago my 84 year old parents moved in next door to my husband and I. Problems started almost immediately. The first argument came when I wouldn't pull the clover from my yard or use lawn chemicals. My grass is always cut and we pull the weeds by hand. I argued until I was exhausted that this was our way and we weren't going to change because they told us to. Then there was the issue with their cat. They accused the nice couple, who live on the other side of us, of trying to steal their cat. It became a constant discussion with them. They practically told my husband and I that we shouldn't be friends with them because of this. When I got upset and said that we would be friends with them if we wanted to, I got cold anger from my Dad, and then the silent treatment. Since then there has been one issue after another. The latest issue is the one I was hoping someone could give me some advise on. Our youngest son is moving to our town and he and his wife have been looking for a rental. They have lots of time to find a place and are quite capable of looking and deciding for themselves on possible homes. My parents took it upon themselves today to call someone with a basement suite and set up an appointment for our son to look at it. I tried to tell my Dad that they didn't want a basement suite and that none of us should get involved unless they ask for help. He wouldn't let it go. He got very angry and the whole thing escalated. I told them to mind their own business. Of course they don't understand boundaries and now I'm going through the exhausting angry silent treatment phase again. My husband and I are fighting over them. The stress is causing unbelievable stress in our marriage. My father can't have a normal conversation; he lectures instead and he's incredibly angry. I used to love being outside in my yard but now I spend more and more time inside so I don't have to talk to him. I feel really terrible now. Guilty and ashamed that I got so angry. Do you have any advise? I'm at the end of my rope. They help the grandchildren occasionally with money, so I think they believe this gives them a say in their lives.