I'm sorry for your loss. These must have been such tough months. I'm glad you had a family business to turn to and are able to live near your folks at such a difficult time.
As for your daughter, the most troubling statement was "...saying she wanted to die so she could be with her father."
Please take that statement seriously. Act on it to help her before she decides to act on it and possibly harm herself. That one statement alone should be the red flag that gets her to therapy immediately. She really should be evaluated for suicidal thoughts and might even need inpatient treatment--shaking, crying, talking about wanting to die, all are far from normal fear of a new school. She fears a lot more than school. Her mind is on her father, not school or friends.
I would not let her walk to grandma's on her own right now, or be at the house alone; even if she's not truly suicidal (and you don't know that for sure yet), she needs watching. She is in a very dark place and no longer has any of the friends, teachers or other support she left back in Virginia.
You mention that she "won't help herself" but if you have ever seen anyone really deep in the throes of depression and grief -- I have -- there are people who just can't get their heads above water enough to "help themselves" and if others don't take charge, they will drown. They can't get out of bed long enough to eat a meal, much less go outside, take on new responsibilities like work or school, and distract themselves out of depression. That's where you as the parent step in and help her until she has the tools again to help herself.
Please listen to your mom and find a therapist this week. Therapists will tell you that certain major life events are intense stressors: A death or a move are two of those events and your child has undergone both almost at once. Her father sickened and died very quickly, and before she knew it she was leaving every place she associated with him too. So for her this is not a clean slate or new start as it might be for you or her siblings. She may see this all as being ripped from the places or people she associated with him.
I"m not saying that as criticism of your move -- you have extremely valid, realistic and healthy reasons for it, but you as the adult can see that and separate your emotions from it a bit. She cannot see that or do that yet. Try to think like she's thinking, not like you as an adult would think.
Please don't think of therapy in terms of cost here. The statement "I don't have extra money to spend for her to go to therapy but not to talk" sounds as if you are expecting her to come out of her shell fast to justify the expense, and as if you feel she's not "helping herself" enough. Therapy takes time -- she has to open up to that therapist, which means she has to have time to build trust, and if you are worrying after every session whether she's talking yet, she is only going to clam up more. If money's really tight, there are doctors who charge on a sliding scale or who will set up payment plans. Good therapists don't want to see a teen, who has been through what she's been through, go without treatment just because nobody inquired about a payment plan. Your mom might also help pay. I don't usually advocate borrowing but this is the one time I would, if it were essential.
Be aware, you may have to try more than one therapist to find one who works for her. Please don't let the cost stop you from trying. Seek ones who specialize in grief in teenagers, most of all.
Go see the school counselor (alone, yourself) today. Not tomorrow or next week but today. The counselor should want to see your daughter tomorrow--ask for it. On your private visit with the counselor, talk about the best way to get your daughter into school. The counselor might recommend starting with just a tour of the school, with you along, and brief meeting with teachers and the counselor before anything like a full day of school happens. The counselor also might identify a girl your daughter's age who could act as a kind of "student guide" for her -- someone to show her around, sit with her at lunch the first day or week, etc. Believe me, counselors and teachers do know kids who make good ambassadors for the school, and who would be sensitive to your daughter's situation (but dont' worry, no counselor is going to tell any student the details of your daughter's issues).
I'd expect your daughter to act out or possibly get very upset and emotional at school. That may be another reason she's avoiding it -- she might fear that she will break down there in front of total strangers, so she'd just as soon stay home. Talk to the counselor about how the counselor or teachers would handle that. Any teachers she has MUST all know about her situation, I think. Teachers can be very kind and helpful in cases like this if they know what's going on behind the scenes with a student.