I'm going to tell my mother that I am not going to sneak around the house to accommodate our muslim house guest as the lady doesn't want to be seen without a head cover thing
Have you tried telling her before?
She always refused to understand my point.
Your house guest is a guest, and you are the host who is supposed to make them as comfortable as possible. You need to respect who they are and their religion, or you are poor hosts. They deserve love, understanding, and respect, not hatred and ignorance.
I don't want them to think I cant be trusted.
They might actually be more trusting if you show them some respect. She might only take a few moments of going from place to place trying to keep her modesty. Have you talked with her about it yet to try and coordinate something?