He has no reason to be at your home unless invited or given permission. If you have asked that he not come to your home for any reason then you have the right to contact the local police department any time he shows up uninvited. This is called domestic tresspassing and it can also show documentation of how often this happens.
I suggest that you make the request in writing so that you have backup to show that you have made this request. He is not allowed to stalk you because you had a personal relationship. Stalking is illegal regardless of the relationship between the parties.
The only thing about a no contact order is that it can sometimes add fuel to the fire so to speak and make matters worse. If you have to meet to “exchange” the children during visitations then a no contact order, while it sounds nice, would not work unless you continually had someone else drop off and pick up the children. My suggestion is to requests that the visitation drop offs and pick ups take place at the police station.
The best thing to do is to keep documentation of this and anything else.
I have a friend who has a camera outside and a monitor that shows his driveway so he knows anytime someone pulls up at his home…it’s a minimal cost for peace of mind and it’s legal.
Realistically though, contact with the ex is likely to become less after the divorce. Normally, during the separation year it’s more of an issue as everyone gets used to new “boundaries”. I suggest sending the request in writing. Be firm in the request that he respect your privacy as he has asked that you respect his.