Yes, this is very normal. There are a lot of huge changes that have happened. She is used to being only with family and she is still 2 so she is also probably having some separation anxiety also. Dad leaving and not seeing her was the first big change. You need to see if he can at least send her photos of himself and make a few calls to her.Do not have him make promises he cannot (or will not) keep.
Your mother being completely gone is also a huge difference especially if your daughter has spent the majority of her "awake time" with her all of this time. When your mother is not there, your daughter, just thinks she is gone forever. This may be the root to lots of this.
If your mom is still in town, allow your daughter to see her as much as possible and let them speak with each other on the phone. I would even suggest your mom actually call your daughter while in the same room, so your daughter can SEE that she is talking with grandma. You guys also need to play "taking care of Great Grandmother" so that your daughter can understand that grandma needs to go and take care of great grandmother. This will gear your daughter up for when your mother is totally out of state. Does your mom have a computer? Can you 2 try out SKYPE? It is a wonderful way for all of you to communicate with live feed of all you talking back and forth.
Does your daughter have a lovey? She can take it to daycare to keep with her. You will need to keep her on a very strict schedule when you drop her off. Give her a hug, a kiss and tell her you will be back when you get off from work. Then you need to hand her to the teacher and leave. Do this everyday. Your daughter will be fine, I promise. Do not make a big deal. Do not make a lot of promises. When you pick her up do not ask her about the crying, focus on all of the fun things. Who do you sit next to at lunch? What did you eat for snack? I like your picture you painted, What was her favorite color today? Take a camera one day and take pictures of all of her friends. When you get home have her tell you about all of the kids. Their names. Then have her tell grandma about it so that grandma will know who she is talking about when she is gone.
On the weekends see if some of the parents and their kids from daycare would be willing to meet at a park to play just for an hour. This will make a new community for you guys. Also see if there are families with young children in your neighborhood. We really did enjoy spending time with the other families in our neighborhood. All of the kids played together while all of us parents supported each other. Many did not have families in town or state so we all took care of each other.
Hang in there. It is hard to see our child cry and not be able to leave them with a big smile. But I promise you will get there. Just keep it together till you drive away. When you get to work, is there anyone that can give you a big hug? I used to go to work and have some nice older ladies that loved to give a big hug to whoever needed one. They really helped me when I went back to work.