He carried out a “brutal” attack at the family home while the children were there.
The children are currently in the care of social services but a letter that Radio News Hub has seen from Hampshire County Council says despite the crime Mr Dyson is allowed to make decisions about who his children can and cannot have contact with.
Ms Simpson wants them to be able to see her, her family and their half brother, who she has care of, and who up until the murder was living with them.
She says he “doesn’t deserve” to keep his parents rights.
She’s now set up a petition to strip killer parents of their parental rights.
A Hampshire County Council spokesperson said: “While we do not comment on individual cases, we can confirm that imprisonment does not automatically restrict or remove a parent’s parental responsibility as defined by the Children Act 1989.”