Wow. I'm guessing she's 2.5 or older, wanting life her way every minute of every day. Well, this is your teaching moment, on many levels. And, don't be sorry for losing your temper, you have a right to have your child behave.
In dad's defense, if he's somewhere where there's a cell phone blocker he CAN'T answer your calls. Also, somewhere along the line people decided that if a person carries a phone they're obligated to answer it NOW. Ummm, no. That's why we can turn the the ringers off, divert calls to voice mail, (not saying he did this) etc. IF you haven't previously talked with him and told him that you expect him to answer your every call you seriously can't expect him to know. If there's an emergency you need to leave a message and tend to it, as it would take him hours to arrive home anyway. And, sorry, there are times it's impossible to comply. That's why we can leave messages and send texts. This is something you could explain to your daughter, "Daddy's busy and can't answer right now, but that's OK, we're going to leave a message and tell him we miss him and love him and we'll talk to him later," and smile to show her it's OK. And don't keep calling or texting, wait on him. Children are teachable, regardless of the parents who think they're incapable of understanding and modifying their behaviors at a young age, and it's our job as parents to teach them so they don't grow up expecting their way all the time as if they're the only ones who matter.
Hitting and throwing things are totally unacceptable behavior for any child, any age, and if you don't get a handle on it now you won't have a prayer later on. It's OK to get angry, we all do from time to time, but it's definitely not OK to get violent and destructive, that's when we use our words. What do you think would happen if she did that in a store, restaurant, or a school setting? That they'd ignore, laugh or shrug it off? First you'd get the bill for damages and then a strong suggestion to take her to a mental health professional. And God forbid she hit another person in frustration or anger, yikes! Then you'd have to deal with an angry parent, and rightfully so. Talk to her and tell her in no uncertain terms that you are very upset with her behavior, and that she is never to do that again. Explain that from here on out there will be consequences for such behavior, something that will make her really think about doing the same thing again. (I'd also give her at least a small consequence for today's behavior, like no dessert or TV the rest of today.) Many parents think a time-out is a consequence, but if it doesn't make YOUR child stop unacceptable behavior it's useless for them.
Tell her when she is sent to her room she is to sit on the floor, bed or a chair, cry if she wants until she stops, and that screaming, (which is only acceptable when she's in trouble or hurt to alert you) hitting, banging or throwing things is never allowed and gets a consequence. She comes out when she's called you and received permission to come out, at which time you talk to her about her tantrum, discuss consequences for the behavior, "You know you just lost your trip to the park this afternoon, and you need to clean your room" etc., then hug her to let her know of course you still love her. (My eldest always asked me, "Mama, do you love me?" when he misbehaved and I always said of course I do and hugged and loved him, but he still had the consequence.) The fact that she said she was sorry shouldn't relieve her of consequences, it's just the beginning.
Seriously, she needs to put her room back in order, (if she pulled the mattress off you can help her with that) and I would make a mental note of what she threw or damaged and remove it from her room and place it in the garage, including clothes and toys. Putting them back should be contingent on her improving her behavior over time, and adding it back one item at a time. This may be the first time she's done this, I don't know, but that would be all the more reason to take things out of the room so she sees the seriousness of this. And, remember, making a special treat for her or taking her somewhere special today is rewarding bad behavior in her mind, even though you may think you owe something to her for your behavior, (you don't) which will increase the likelihood of her repeating today's performance.
When you talk to dad remember, none of your behavior or your daughter's was his fault, so don't make any accusations. Accept that in the future you can ask him to answer, but know that he can only do what he can do. And, he's entitled to his free time.
Also explain to her that we can't always get what we want, and that she has to accept that. Being spoiled about it isn't going to get us our way in life, and that's as it should be, we are but a part of the world, we don't own it and it doesn't owe us. The only thing a child is owed is the love, care and discipline of their parents.
Like I said, you have many teachable moments to act on, unless you want a life filled with turbulence.
God bless<3