What is the appropriate advice for balancing the care of a sick mother residing in another country with the demands of family and professional life, in order to avoid shortcomings and feelings of guilt?

May Allah reward you for your eagerness to honor your mother and be good to her. If you do not travel to your mother every month, you are not being disobedient or negligent towards her. As long as she has someone to serve and care for her, it is sufficient for you to maintain regular communication with her through phone calls and to check on her. Your visits to her should be within your means, so as not to harm you or prevent you from fulfilling your duties towards your husband and children.