Be careful who you date. See what 'vibes' they get from the person. Ask about his family. It is also for your safety, your sanity, and your reputation in court, if your ex-husband is still stalking and gathering information. Once you've been involved with a stalker, you'll probably feel you need help in determining who a 'good person' is, anyway.
Life goes on and the kids get older.
You might want to wait to 'live' after all this has 'gone away'. As difficult as it is, pretend with them for a while each day that things are normal. This is not just good for them and for you, but will show later on if you get into court that you are a good parent. Put their needs close to yours. Make them feel safe, no matter what .