This seems more of a not knowing you well issue than a problem with the child. I would try to spend some more time with them maybe invite them to come for dinner or invite your mother in law to go shopping with you. When they know you are comfortable and they also are they won’t feel weird about inviting you when your husband isn’t there.
Best thing to do. Ask him what he wants. Apologize. Tell him it was a reasonable request and you should’ve put his cooking first. When he softens, tell him you dont want to fight or argue. Then ask for help with your work. You might be surprised. Often. Older folks I am one) are desirous of being young like you, and need to live their memories through you. Understand life is temporary, and you need to see the future just as much as he needs to see his past. In understanding one another, and putting one another first, we mature and become adults who care. See your parent as someone who is desperate to live a bit longer through you. Life is but a short time. Do it without conflict.