You have been divorced not even a year. Give yourself time to heal, recover from the trauma, and give your daughters that time, too. Your situation is not unique. I have a friend who went through the exact same thing. She has one daughter. I am always angered when I hear of fathers who walk away from their families. All I can tell you is that you cannot make a man be a father to his children and, unfortunately, some men do not recognize their importance in being an active parent to their children. You cannot change that. But, you can do something to empower yourself.
1. Teach your children that life is not fair, but there is hope in all situations. Dad might be gone and absent from their lives, but someday, he might realize he made a mistake and try to make things right in their lives. We all must learn forgiveness at some point in our lives. Better to learn now, because it's really for our own peace and mental health. When he realizes his mistake, they can decide at that time how much they want him in their lives. Meanwhile, it's probably best that he's gone if he cannot stop hurting the family.
2. Teach your daughters that this is not their fault nor your fault. Sometimes, people choose activities that hurt not only themselves but the people they love. It is selfish, because they are only thinking about how good they feel in the moment and do not stop to think about the pain they cause. It is the same with addicitions, negative hobbies, disobedient behavior. Take this as a time to each them the importance of listening to advice when you are instructing them against activities that are harmful.
3. Teach your daughters that they cannot fix the problem. Not their job, not their duty. They cannot be smarter, prettier, more obedient, more whatever. Those are not the reasons Dad left.
4. Teach them that they are beautiful and you all deserve someone who is going to be totally connected to your family. You also must believe this. Infidelity has nothing to do with the person who is being hurt. Something is going on in your ex's life and mind that has caused him to believe that this new woman is going to fix everything for him. You cannot have been more beautiful, slimmer, smarter, wealthier, etc.
5. Do not force time with Dad. If he is hostile, he might take things out on them and then you'd have a whole new set of problems.
6. See if you can get help from his family, your family, and friends. Get over the embarrassment. You didn't do anything wrong. Do not be a victim; be victorious. No one deserves to live with someone who will not be true to her and flaunts negative behavior in front of the entire family. You deserve better. You deserve love. Let those who are around you love you. But, be mindful of your responsibility. In this day and age, we cannot be so complacent that we just blindly trust everyone when it comes to our children. Make sure your girls are excited about spending time with Grands, cousins, aunts, uncles, whatever support system you have.
7. Do not bring someone unrelated into the drama of this situation. Do not replace your husband before you and your daughters have had time to grieve it, heal from it, and press forward. Loss of a marriage is probably more traumatic than the death of the spouse, because death is final and, though tragic, it has a natural conclusion and we know we will not see that other person building a whole new life without us. Death of a marriage is painful, unexpected, and we believe avoidable, and can cause similar emotions. Go through your grieving process before dating again. You don't want to dump baggage onto someone who has no idea of your history and a new person cannot fix the pain your ex has caused.
8. If your ex remarries, teach the children to be polite and respectful to elders, but they do not have to give their love and trust. They have been betrayed. You have been betrayed. Trust is earned. They can love someone but they do not have to believe everything someone does or says. It's sad, because girls should be able to learn trust and love from their fathers, as well as security, confidence, and determination. You cannot change that, but you can give them an environment in which they are free to grow into confident young women by nurturing their good qualities, being honest, and being steady for them until they can learn to trust adults again. If, in the future, their "step" wants to build a quick relationship with them to make everything alright, teach your girls how to grow up quickly by responding from their heart. If they aren't ready, they should be ok to speak honestly. But, you cannot turn them into pawns by making them hate her, your ex, etc. This is a part of life. Your ex might have more children who will be their siblings. That's at least a few years out, but it's a possibility you might have to confront.
9. Have faith and hope in the love of God yourself and teach that to your daughters. Love yourself, so that they will see what it's like to respect and love yourself. And, loving yourself means taking time to rest sometimes. You are going to need help. And you will have to master your free time. If your daughters are older, you can take advantage of church, after-school programs, clubs, or private companies to keep them busy during your "me" time. Relatives who can be trusted can help you carve out a little "me" time while you recover financially. If your girls have friends they enjoy spending time with, let them visit, but not too much too soon. They are young, yet, and easily impressionable. You need time to monitor their moods shifts and behaviors, and they need some time to heal before feeling like they are being sent away.
It is only a suggestion. I am not a clinical psychologist, though I hope you are seeking some help from a service in your town. As I wrote before, you all have suffered a severe trauma, emotionally, financially, and spiritually. I would seek out some counseling either through your church, a church, or a government office. Usually, there's free assistance in your community when situations like this happen. You'll need to restructure your finances, your schedules, everything. Do not try to be a "Superwoman" and do it all alone. That will make you prey to a man who might take advantage of you. Take time to heal and seek help from those who love you and those who are tasked with helping during times like this. Hope this helps.