My name isXXXXX have been a licensed attorney for over ten years and will be assisting you today.
The money in that account is entirely yours since you have survivorship. It does not pass into the estate, so you certainly have the authority to spend it on final expenses (and the right to reimbursement from the estate if you so choose).
If there was no will, the rules of intestate
succession apply. That means that the assets (once liabilities are paid) will be paid equally to all the children.
As for becoming administrator of the estate, you must first open the estate in probate court. You can request that you be named administrator. If your siblings contest your request, the court will hold a hearing and decide who would be best to administer the estate.
In order to sell the house, you would first have to be appointed administrator. Now what your mother has passed, there is no longer anyone available who has the legal authority to sign the deed for a sale. The only person who would have that authority would be the administrator of her estate.
You would start by filing a Petition for Letters of Administration. There are forms online you can use, such as here
The local court clerk may have forms to use, too.
If you have more questions please feel free to ask. I'll be happy to answer them. If you do not, please do remember to rate my service in assistance to you today.