Nobody in our family has ever been divorced, and I feel really ashamed. Will my children feel the same way?
Changing the way you see your family identity is huge for you. The best way to help your children is to establish a sense of pride in their new family, and to look forward to the future with a real sense of possibility. You cannot possibly predict how your children will feel, but it is your job to help them understand that they are not at fault and that both parents still love them, even if they no longer love each other. It is also important to refrain from projecting your own feelings of shame onto your children. Let them react in their own way, and support them in their reactions.
Your children will witness you overcoming obstacles, demonstrating independence, and moving forward in your life, notwithstanding challenges. You can be a great teacher to them during this time, by demonstrating pride in your family and in yourself.