Your children can claim their father's legal rights in the estate. Assuming your father in law died unmarried their claim would be for one eighth of moveable property between them. Moveable property is all estate except houses and land. I hope that helps. Happy to discuss further.
The heritable estate isn't included because the law doesn't allow for a legal rights claim in respect of heritage. A person in Scotland can leave heritage to whoever they want. As he has elected not to leave your children anything in his will, your children only have legal rights which apply to moveable estate only.
Not where there is a will, no.
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