Don't need to apologise to husband's parents?

Well, if you love him then stay. You shouldn't have told his mom that he lied to her. That was none of your business. Apologize to his mom and when she calls so often, maybe let her know that you both have busy lives and will call her back when it's convenient. Don't get involved with the relationship between your husband and his mother that's his business. Sound like you both need some professional help with counselling and anger management.