What can be done if the executrix of their dad's estate is refusing to distribute what would have been my ex's further share to our sons?

Yes, it is likely that if there is are other assets to be distributed, your sons would be entitled to receive their father's share. An estate would probably need to be opened for your ex so it can receive the remaining assets of his father's and distributed to his heirs. Unless the assets were not substantial, then a simpler proceeding would be needed rather than a full estate. If you need assistance, I would be happy to help.

It depends on the terms of the deceased's will and whether the children are over 18. You can get a copy of the will from the probate court's website. If she's required to make distributions and she's not, you need to get an attorney ASAP. That probably means she's stealing their money and she's probably a deadbeat, so once it's gone, they'll never get it back.