Is the failure to bring over a sick mother considered oppression and disobedience to her, especially if the husband does not agree to her presence for long periods, and that might affect the stability of the marital life?

Thank you for your eagerness to honor your mother and maintain a good relationship with your husband. Not bringing your mother to live with you is not considered an act of disobedience (uquq), because her living with you is not obligatory upon you. If the house is your property, your husband does not have the right to prevent you from bringing her to live in it, as the owner of a property has the right to dispose of it in a permissible way. You must fulfill your husband's rights; his rights take precedence over the rights of parents when there is a conflict. So, be careful that your mother's presence does not affect the fulfillment of his rights. If you are unable to bring your mother to live with you, strive to honor her and care for her to the best of your ability, such as hiring a maid for her or supporting her financially.