Your granddaughter is going through the Tyrannical Three's (as is my 3 year old grandson.). She is "ruling" her mom with her crying, manipulating her, basically having a temper tantrum to get her way. As long as she gets her way by crying she has no incentive to stop the behavior. Children need boundaries or limits in their lives, it teaches them what to expect and actually helps them to feel more secure. A "no" isn't the end of the world, though it seems to her it is.
If Mom has a hard time telling her "no" and sticking to it, ask her what will happen when your granddaughter goes to school and is told "no." Schools and teachers don't cater to children and she will be in for a rude awakening.
Whenever she starts to cry she could be sent to her room to cry alone with her door closed, that sometimes stops children from crying since they have no more audience. When she is ready to stop crying and come out of her room your daughter could then teach her how to use her words to express what she is upset about, and encourage her to use her words BEFORE she starts crying over everything. She can also use this time to tell her we don't always get our way. If she is consistent each and every time eventually (and it may seem likes it takes forever) your granddaughter will grow out of this.