I applaud your not passing on the request, but I think that by lying about what you did, you are trading one unhealthy behavior for another. I think a better course of action is to say Mother, I don't want to be and won't be in the middle of this, this is entirely between you and sister. For any response from your mother than isn't :okay", I'd repeat, Mother, I'm not going to be in the middle of this. You need to ask her yourself if it's that important to you. This is an excellent time for bean dip.
It is perfectly possible to be polite about saying no to your mother, particularly in this case, but lying to her is not polite.