This is a difficult place for you to be in and I want you to know I recognize the struggle in this question.
As for whether God will forgive you the answer is yes. The bigger question is whether you will forgive yourself. We often times associate our negative feelings of guilt and condemnation with how God must feel about us and its simply not true. Romans 8:1 states that there is NOW no condemnation in Christ. So your feelings of guilt and condemnation is from the accuser of the brethren, satan.
Now that the theological concern is taken care of lets discuss the very real issue you are facing with your family. If you have children there will be much more guilt concerning how they will respond with you deciding to leave their father for someone else. Anyone else, even if it was another man, will be seen as the person you chose over them. Breaking up your family for an outsider will be seen as negative by your children no matter how you spin it or how accepting your current spouse feels about the break up. It will take time, lots of time to heal from the breaking up of a family.
Counseling or therapy will be needed for the entire family to navigate through the transition of your family. This is something to seriously consider and look into beginning as soon as possible. You will need a third party to sit with the family and discuss how the transition effects each person, including yourself.
Whether or not you should leave your family for another woman you have fallen in love with is a decision your decision. Choosing to be happy is a decision we all must make and sometimes this requires us transitioning out of certain relationships. You may leaving your spouse but you are not leaving your role as a mother to your children. That's important to remember.
Your relationship with God is the vehicle to carry you through this difficult season. It is a season. It will pass. It is the best of times for your and it is the worst of times, but you can powerfully and thoughtfully make this transition. You can do it with integrity and powerful love for yourself and the important people in your life.
Let me know if this was helpful for you in the comments.