Hey there. I've been through the divorce process... and the re-marriage process... and the divorce process again. It SUCKS, and it's not easy. So I totally feel for you.
Things aren't going to get better within a matter of weeks. Things may not get better after several months, or even after a year, because there are so many emotions involved. As your father becomes closer to his high school sweetheart, and your mom makes the transition from spouse to single woman, you're going to experience new and recurring feelings over and over again. You'll have to deal with them as they come, and unfortunately, "there's no cure for normal". Because these feelings are normal, I can't give you a secret, amazing way for dealing with them, other than finding healthy ways to cope with the stress. Write in a journal, hang out with friends, play video games, go outside for a walk/fresh air, pick up a new hobby, dive into your schoolwork... there are plenty of things you can try in the weeks and months to come.
Now, I know you have a close relationship with your dad - I did as well when my parents were getting divorced. HOWEVER, you are their CHILD. You are not the best friend who will take secrets to their grave. You are not the marriage and family therapist who is bound by confidentiality. Most importantly, you are emotionally involved in this conflict and it is not your place to carry all of these burdens. You have enough to deal with as it is. I know you probably think you have to be strong for your parents, and that you have to be a loyal, loving, accepting daughter... but guess what? You DON'T, and what your parents are doing right now isn't appropriate.
So what I would suggest is to tell both parents - today - that you are no longer carrying their secrets, because they are hurting you. Tell them that if they reveal any more information to you, you won't keep everything inside of you. You'll find an outlet, whether it be the other parent, or a friend, or a school counselor, or even TeenHelp... but make it clear that it's not your job to keep their dirty little secrets under wraps. Tell your dad that you will accept Betty when YOU are ready to do so - right now, I believe it's far too soon to suddenly say, "Yeah, we're Facebook friends, I forgive her for getting in the way of our happy little family." Furthermore, Betty may be your father's new wife in the future, but that doesn't mean you have to accept her as a mother figure - don't EVER feel pressured to do so in order to make your father happy. Do what makes you happy, do whatever it takes to stay sane throughout the divorce process/the aftermath.
I wish you all the best. <3 Feel free to PM
me anytime if you want to talk. Like I said, I've been there before. Twice, actually. =P