Without your father in the picture, then this situation is very cut and dry. Since you are the beneficiary of the pension, then no one else can challenge you for the right to get that pension. When a beneficiary is named, it is set in stone. Even if your father had survived long enough to be given the pension and then named you the beneficiary, you would still have legal right to it over your step-mother's sister.
It is important that everyone updates their will when a major event such as a spouse passing away occurs. It can often clear up issues that can otherwise become troublesome. However, in this case, no you cannot touch that money to pay for the funeral. As a guardian, it is your job to see that the money is used to the benefit of the child and not for estate expenses.
It is common for parents to gift large parts of their estate to their children each year to see their children enjoy the money while the parents are still alive. Each year, the federal government sets a maximum threshold for how much can be given as a gift without tax. As long as the checks are made out separately to each of you, then neither you nor your father owe any tax. However, it can get complicated if you start using those funds for yourself. It is best to set up custodial accounts for your children and keep them separate from your own account.
Each state has a small estate amount that acts as a barometer for how probate works for certain items. If the house falls below the small estate threshold and there is no will, then the house would be left to the surviving spouse. If there is no surviving spouse but there is a will, then the small estate would go to the beneficiary mentioned in the will without probate. But if the house exceeds the small estate limit, then it would have to go through probate.
If you are made the trustee of a revocable trust where all of the trust members are gone, then your job is to make sure the income from the trust is reported properly. The catch is that you can no longer use any of the social security numbers of the trust members because they have all passed away. You need to get a new tax ID number for the trust before you start distributing funds.