Is it permissible for me to take commingled money from my father to open a shop, knowing that most of this money comes from Riba-based loans?

There is no harm for you in benefiting from what your father gives you to open the shop, because his money is mixed, and dealing with mixed money is permissible, though disliked. Also, the prohibition of a usurious loan pertains to the borrower's liability, not to the money itself. You should advise him to sincerely repent from usurious loans and to hasten to rid himself of them by accelerating repayment if the interest is waived or reduced.