I think you have, once again, done too much for people, and I am concerned that you are not taking care of yourself.
Maybe this stepbrother feels guilty that he didn’t do more, and maybe he’s just been sitting around waiting for an inheritance. I don’t know. But you don’t have to feed into it.
I would direct him to the funeral home. They are professionals and they are experienced with the treatment of human remains, and the laws around transport. The cremains belong to your mother. If your mother is willing to share them, then it’s up to your stepbrother to arrange for (and pay for, frankly) an appropriate container of his choice and the shipment. I doubt he knows what the customary quantity is, and he will be content with what he receives. But let the funeral home handle it – they know how to deal with fractured families. Just text or email your stepbrother – don’t get into a long phone conversation which he will fill with demands and guilt. Tell him your responsibility is your grieving and elderly mother, cleaning out the nursing home room for the next resident, and much more.
I would also tell him he is free to set up whatever memorial service he would find meaningful, and to choose the date, location, clergy/officiant, music, public notice, invitations/notifications and other details. Say that you are dealing with your grieving mother who does not have the stamina right now. You also have a special needs son who is dealing with the loss of his grandfather.
Don’t worry about not notifying anyone else. Any kids who wanted to be involved would have left contact numbers with you or your mother or the nursing home. Period.
Now, be prepared that he will also start asking for possessions, and a portion of the estate. This happened to my MIL when my FIL died. It was awful. Direct your stepbrother to your father’s attorney (assume he knows the name – don’t volunteer it). And give the attorney a head’s up. Do not get involved in this. Say much less and do much less than you might.
I also would not engage in a discussion about what Dad would have wanted. Funerals and memorials are for the survivors - so your mother should do what she wants, when she wants. Your stepbrother can do what he wants, when he wants. Be kind, but don't get overly involved in his problems, his grief and perhaps his guilt for not being around.
You have to take care of yourself – it’s enough that you are taking care of your mother, your husband and your son. Stop and let the other grown-ups be grown-ups.