"To anchor" means to put something somewhere that is solid and unmovable. This verb comes from the noun "anchor" which is a very heavy weight thrown over the side of a boat when the people in the boat no longer want to keep moving. A common sentence for sailors is, "let's anchor here for the night". This means that they are going to stop travelling and rest in place for the night.
"Marital bed" is a bed shared with a husband or a wife. If somebody moves out of the marital bed and into "the girls room" it can mean several things. It could mean that there is trouble in the marriage, so they don't want to share the same bed any more. It could mean just that Mammy moved into another room for any number of reasons; to sleep better, the marital bed is uncomfortable, or maybe the husband snores?