It is very serious matter. Everything was going well but your ex. messed up everything due to jealousy. It seems your BF loves you but also make himself ready to accept your past and it is obvious. If you want your Bf back then you should talk to him and assured that there is nothing in between you and your ex. If he really loves you then he will understand you and come back to you.
If he will not do so then it will be better to live alone with your kids and give them a better life.