My son passed away recently and he has been ill and lived with me. He had joint custody of his two boys, 11 and 12 years old. We had them with...

I am very sorry for your loss, and it must be even more difficult to not have the comfort of your grandchildren now or to be able to comfort them.  I am unable to give you any specific advice because grandparents' custody and visitation rights vary from state to state, and it is unlikely that I practiced law in your particular state.  I can share some general thoughts on the situation, though.

First, there really are no standard rights for parents or grandparents.  The standard in every jurisdiction to determine custody and visitation is always the best interests of the child.  Many factors go into this, as I'm sure you realize.  For example, if the boys' mother is working long hours and does not spend a great deal of time with them, it is likely that time with their mother would be considered more in their best interests than time with a grandparent.  If the boys have many extra-curricular activities and time with you would interfere with those, that probably would not be considered in their best interests.  On the other hand, they are of an age where their own preferences might carry some weight, and if they express a desire to spend time with you, a court may very well find it is in their best interests to do so. They are also accustomed to spending a great deal of time with you, so the court could find that what you seek is in their best interests because it is less disruptive of their lives.  But I don't want you to pin your hopes on the fact that there was joint custody when both parents were alive and the boys lived with you.  Now there is one parent who has sole custody under the law, and you cannot step in as a substitute for your son. 

As someone who did custody work for a while, and as a parent and grandparent, my thought is that what you are seeking certainly does not seem unreasonable, but how the court determines the best interests of the children is going to depend on many variables that I do not know and probably variables you don't know either.  My best advice to you is to check with your county bar association for a list of attorneys who practice in this area.  Often, attorneys have an arrangement whereby if they are chosen from this list, they are willing to provide an hour or so of advice at a lower than usual cost.  Also, you can check on the laws of your state with the link below.  What you should also bear in mind is that the court will do everything possible to try to get you and the mother to work out an agreement you can both live with, without the trauma of litigating any of this.  Most cases do settle, and the odds are with yours being worked out, too.  I wish you the best of luck with this!