Tough times is right - is your family aware of your part in the situation? Sounds like your mother is using emotional blackmail to control what you do - not good. Did your girlfriend exchange hurtful words with her? Is your family trying to protect you or are their feelings more personal towards your girlfriend? How did they feel about her before this happened?
Bottom line is you're a big boy and need to solve your relationship problems with the person they're with - best not to involve your family or friends. If this is an important relationship for you then let your family know so and assure then that you will not drag them into your problems in the future. Remind them that you were largely responsible for what happened. Also tell them that you appreciate their support of you and that likewise you don't want this relationship to come between you and your family. If they see that you are happy and having a good relationship with this girl they *should* let this situation go. It may take some time - and your girlfriend may have to make some ammends if she took any shots at your family.