There's NO GUARANTEE she'll EVER want you back, but if she does it will be:
1. Because you respect her and her decisions. If she is dating someone else now, let her go. There MAY be a chance in the future, but you being a pushy jack-azz NOW will NOT improve those chances.
2. Always show your EX-wife that you respect her as the mother of your children, as a good woman, as a wonderful person.
3. Be a supportive co-parent to your ex-wife. Be willing to go the extra mile to help her with the kids (pick-up early, drop off late, etc.)
4. Do NOT be her 'friend'. Do NOT be the shoulder she cries on about man troubles, etc. You're NOT HER GIRLFRIEND...you don't want to be put in the 'friend zone'.
5. Go about your business in a mature manner. Live your life as the kind of man she would admire. Say what you mean, do what you say. Get yourself in shape: physically, mentally, spiritually.
6. Be the best dad you can be to your kids! They deserve it.
If you do all of the above, it WILL MAKE you a more attractive partner/potential partner. SHE may never choose you again, BUT you WILL attract better/more stable/more mature partners who can help you and your children BUILD A GREAT LIFE...and that's better than you're doing now, yes?
Good luck! Make yourself a 1-, 3-, and 5-year plan to improve your life (write it down!), then LIVE IT!