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Your question was transferred to relationship so I will be help you further with your question. It's hard to move on when you have unresolved feelings for your ex, especially if they continue to tell you that they love you but from what you have told me about your ex he isn't showing you much respect to talk so negatively about you to his now girlfriend and allows her to taunt you without saying a word. What you are going to have to do is accept that the relationship is over and talk to your ex about the way you are feeling about how he has treated you and continues to treat you and you also need to learn your self worth and realize you deserve so much better than he is giving you. I think the fact that you were together so long plays a big factor in this and why you cannot find the closure to move on to someone that will treat you better and care about your feeling enough not to allow someone to constantly taunt and disrespect you. Moving on after a break up can be very difficult, getting over someone you have loved can take time and can be very draining. It seems that your life comes to a stand still and it may stay on your mind constantly.
There are three crucial steps to moving on when you break up with someone you invested so much time and feelings into but it can be done if moving on is truly what you want and closure to be able to move on. You need to accept that the breakup is final. Don't sit around and wait for him to come back to you. Chances are that this is not going to happen because he is in another relationship now. Try not to blame anyone for the breakup, including yourself, this will only leave you feeling bitter. You also need to grieve the breakup. Give yourself time to do this as it is a necessary part of the healing process. However, if it causing you too much pain try to find other things to keep yourself busy to take your mind off of the breakup. Go out with friends or do something that you really enjoy doing to help you move on. It's too soon for you to start dating and you should make the timeline for getting out and dating only when you have found closure in the relationship that you had for 16 years with this man.
If you do decide to date again make sure that you are ready for this and do not allow the previous breakup to scar your future relationships that is why closure is very important you don't want to take your old baggage into another relationship and repeat the cycle you want to be able to start fresh. You may decide that you do not want to date again for a while and that you are happy with yourself being single but it won't be productive to continue to be alone for a long period of time, whether it be you hanging out with friends or family, volunteering, accept more work hours, just as long as you are not sitting at home pining for your ex because to be honest it doesn't sound like he is pining for you since he is with someone else. It might be hard to hear but if he truly wanted the relationship back he would have stayed by himself for some time and talked things out with you. You have to realize that you are worth more than he is giving to you and that you deserve to be in a healthy and loving relationship with someone that cares about you and loves you.
Also counseling may be important for you to help you get through this grieving process and better move on without feeling like you were thrown out like yesterdays trash which brings me back to learning your self worth and not feeling like you can only be justified by your ex. The fact that you are already being asked out on dates shows that you have something to offer someone. I think it may be the fact that you have accepted his treatment for so long that you started to believe that you didn't deserve any better but you do. The fact that he treats you and your children second best shows that he has alot of growing up to do and is being very selfish and you cannot make him be a better father he has to want to be better for the children. Counseling for both you and the children may be a good idea so that you all can heal from this.