My question is: being my mother ADA, the House belongs to her or should be split between the other two kids? The other child may refuse to give us to my grandmother's death certificate?
The lasting power of Attorney given by your grandmother to your mother went with her death.
Anyway, she didn't have the power to make the transmission of good. If your grandmother wanted to leave the House to your mother, she would have made a will.
Still, if the House was your only asset she could not have left the property to her since he had two other sons, who are heirs needed along with your mother and must also receive part of the inheritance .
By law, your grandma could have left up to 50% of your equity who wished, if it had expressed in a will. This is the so-called heritage available.
The other 50% of the equity, however, must be divided between the heirs, who are the spouses, children and parents, for example.
Therefore, the transmission of this property will be made to the three children equally (since there was no Testament) through judicial or extrajudicial, inventory held in the registry (see the step by step from the inventory type).
On the death certificate, this is a public document and so just go to the civil registry office where it was made and ask for a duplicate.