Let me try to make this as simple as possible for you....
#1) Be thankful you have good in laws that are willing to help with your child. This is a grandparents resposibility and joy.
I know lots of people who have no support of any kind. Its rough.
I have a 5 year old daughter, she is awesome, but some alone time to just relax and catch a buzz or have some tea is also awesome. No guilt there. At all.
If you didnt get a break like this you might freak out. So enjoy it. Just remember to give thanks to the in laws.
#2) As for the guilt about you dad, this one is easy. You owe him nothing.
He most likely had a breakdown because he knows exactly what he did and has a hard time living with it. Not your problem. He got what he had coming.
Let it go and move on.
#3) Your Mom. Honestly, its nice that she wants to be a part of her gandchilds life. it is. However, if she can't conduct herself in a respectible way, what is the point of you having to just deal with it. I would say something to her about it. Or distance your family from her, eventually she will notice and ask about it. When you tell her the truth, it may hurt her feelings, but it may be the only way to really get it through to her.
Do yourself a favor, get the in laws to watch your child for two days and have three glasses of wine. You deserve it! really! Just be sure that you tell the inlaws how much you appreciate them and how refreshing it is to have someone like them in the picture.
From what I can see, you are a very responsible, honest, and caring person. Your child is lucky to have you and your husband. I know some pretty lousy parents.
One more thing. Cherish every moment you can with your child at this age. it goes by quick and then they are talking back to you.