How much did Mom pay for the funeral?  How much are the tax refunds?  Has she been reimbursed from any other source for her expenses, including your fee for preparing the returns?  

Distributions to intestate heirs are made only after creditor claims, final expenses and administrative fees are paid.  As far as I know, that's the law in every state.  The question is whether Mom can truthfully sign a statement that she "will pay out the refund according to the laws of the state where the decedent was a legal resident."  If she pays them out to reimburse herself for the funeral and tax return preparation costs, she's following the law.  The check will be issued in her name, if it's on the Form 1310,  Some people have problems with electronic filing on decedent returns, you can make your own decision on that.  

In fact, she could collect the refunds with the Form 1310, and then distribute any money left after priority claims to the grandchildren.  That's one of the purposes of the 1310.  If an heir is unwilling or unable to file the return (for example, if they are three years old) then some responsible person can step in and close the books with IRS.  That person just has to promise to do the right thing with the refund.