First, the assets will not go to the state. If there is no will, they will be distributed to the living relatives according to state law. Depending on the size of the estate, that is, the total of savings and 401K, it may be best to set up a simple inter vivos (living) trust that names the beneficiaries according to the mother's wishes. If the estate is relatively small, it would be simpler to have your mother write a basic will which describes the distribution of her assets. A trust would avoid probate. To set up a trust or a will, it would be best to consult an attorney to make sure it is done properly.
Your husband should talk to your mother and explain the financial issues. She should understand that if she dies without a will or trust, she would be causing significant legal and personal problems for her children. She can name one of her children as the executor of the will, or the trustee of her trust, although it may be best to name more than one as co-trustees. The son she considers most responsible should handle her affairs. She should decide how to divide her assets among her children without undue influence from any one son.
You will not get your husband's brothers to understand that you are not rich. They have no reason to consider your expenses, child support, etc. any more than you should consider how they live. They should discuss the situation and come to some agreement. The funeral expenses should be paid from the estate assets before the estate is divided according to the mother's wishes.
As for funeral expenses, your husband and his brothers should deal with that issue right away, not leave it for the time after she dies, when emotions run high and funeral directors can take advantage of the situation. Cremation is probably the least expensive alternative. If that is not acceptable you should explore alternative services to get an idea of the costs involved.