Can I take my grandmother to court if she did not turn the house over to me as per my dad's request?

If he did not have a will, you may be entitled to the house depending on whose name it is in. You may be your Dad's heir.

What your father said, and what he did, are not the same. Because he died without a will, his property that he owned at death will pass under the laws of intestate succession. You need counsel to assist you in sorting out the distribution of his estate and closing out his final expenses.

You may have a major problem since nothing was reduced to writing. Your grandmother can also say that your grandfather wanted everything to go to her. By law, your grandmother is in first position. Is there a will or community property agreement? Without anything in writing, you have an up hill battle. One you will probably loose.