In the will it states how she wanted her assets divided among the family which include money she had left in the bank. But however her daughter who has her named on the account refuses to carry out my grandmother wishes is this legal
Potentially, if your grandmother and her daughter were joint owners of the bank account (which is also called "joint owners with the right of survivorship" - check the paperwork that was signed when the account was opened, or when daughter's name was added to the account). In such a case, when one owner dies, the money in the account goes to the remaining and surviving owner. If that occurs, and there is no other cash available elsewhere, then the testamentary wishes of your grandmother cannot be fulfilled.
For example, if I write a Will and leave $1,000.000.00 to my dog -- but I don't have $1,000,000.00, or any money at all -- then the intent of the Will can't be carried out. Likewise, while your grandmother may have intended to distribute cash to named beneficiaries named in her Will, if the account was a joint account with her daughter, then the money becomes her daughter's upon grandmother's death.
But that's not necessarily 100%. Depending how much money you're talking about, it's worth having a consultation with a competent probate/estates attorney. If you're dealing with $50.00, it's almost certainly not worth it. But $50,000.00 would be.
Best of luck to you.