I would not say that you have gone wrong, at all. The problem is that you do not have priority to petition the court. You are not one of the heirs. You are not even an interested party, under the court rules. What needs to happen next depends on the value of the assets. If the total value is less than $20,000, then probate is not necessary, at this time. Assuming the assets are worth more than that, then probate would be required.
A conservator needs to be appointed for the minor children. That person would then have priority to petition to open an estate. I believe the first step would be to have a conservator appointed and THEN open an estate. The alternative would be to have one of the county public administrators handle the estate. This would probably result in more costs and fees than you would experience probating the estate yourself.
Please feel free to contact me if you have any additional questions. I would be happy to assist you in any way I can.