A family member found John David Bound, 59, and Gwendoline Christine Bound, 80, dead at their home in High St, Abergwili, Carmarthenshire on 26 March.
Mrs Bound had been shot in the chest and Mr Bound had head injuries.
Their inquest in Llanelli heard he had told relatives he was worried about lockdown restrictions.
He had said he was concerned restrictions on leaving home would affect his ability to check on the welfare of his animals and he had said "he didn't know how he would cope", the hearing was told.
Mr Bound, who was known as Johnny, was "devoted to his mother" and that she often said "she would not have been able to cope without his help", the hearing was told.
Mrs Bound, who was known as Christine, was well-known in the area and had worked in the Post Office and the sweet shop.
Mr Bound owned three shotguns and two rifles which he used to control the rabbit population on his smallholding.
Acting senior coroner Paul Bennett said: "There must have been something that triggered John to get his shotgun" but added there was no suggestion it was "premeditated or planned".
He concluded Mrs Bound had been unlawfully killed and Mr Bound's death was suicide and said the deaths had "undoubtedly left their family utterly devastated," adding: "I hope they are reminded of how they lived their lives and not how they tragically died."
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