I agree w/Peace...get your kids into therapy as soon as possible. There may come a time, very soon, that you will need to have that talk w/the wife about bad mouth talking about you. She's using the kids to get to you and yes, to turn them against you. Try to explain things to them in the simplest way and then let it go. You do not want your children involved in what is going on w/their mother. If she brings up matters that are between you in front of the children again, just say "wife, if you want to talk, we can arrange a meet up and talk, but I will not discuss our business in front of the children". You could also say, "I will be happy to talk to you after the holidays and when the children are not here to hear our discussions".
I would advise my lawyer of what has been happening and the conversation that took place w/the children. For the time being, be the best actor that you can be. You may like her behavior, but she is still the mother of your children. Try to smile and be upbeat around her for the time being. The old saying "kill them w/kindness" is very true in a situation like you are dealing with at the moment.
I realize that she is living in the home that you both have lived in, but you moved out, therefore, it has become her space. Since she mentioned knocking or using the doorbell, then do so. It is now her space, as well as the children's. You wouldn't want her barging in at your new space w/o knocking. Honor her wishes for the time being and respect the boundaries she is putting in place. She will need to do the same if you put boundaries in place.
I know you are not happy w/her behavior, but you are going to have to dig deeper for patience and be the best actor you can be for now. Get a rubber band and put it on your wrist and every time you are tempted to say something, snap that baby and feel the sting. That should turn your focus to that wrist.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.