I have two advises for you :
Don't trust your SIL words no matter how close you are to her and how much your trust her. I have a very cunning SIL and she does the same , she tries to befriends with me by initiating converstaion against my MIL and then act very childish infront of MIL and very innocently tell things to her with added spices. Don't expect any goodness for yourself from your SIL may be she is lying to you just to make u upset or to cause trouble b/w u and ur husband or b/w u and ur MIL and I think she has been successful till now right ?
Even if your MIL is saying negative things abt u behind ur back always always remeber when you point a finger towards a person rest of fingers are pointing towards you. People are not stupid these days and plus this is what I think when I go thru a situation like yours that Gheebat is forbidden in Islam and this Gheebat who so ever does it will be answerable to ALLAH for disobeying ...........and 2nd people will talk ill just because of anything in your your life / out od jelousy it could be bcuz of your husband , your kids , your looks anything in the world that u cannot even think of . You can never staisfy every person in this world or as a matter of fact every person in your family let them be dissatisfied and be upset you ...why are u upseting yourself ?
I am going to add to this by saying:
Your MIL is your MIL...not your mother. She can never love you the way she loves her son or forgive you the way she forgives her son. So dont expect it from her. This exact same philosophy applies to every single member of your inlaws' family.
The best way to counter this is to be an angel. Im DEAD serious...be a freaking angel and show everyone around you how wrong she really is. Never answer back, call her AMMI, be polite to her and SUPER POLITE in front of others, do khidmat as much as you can, call her regularly, ENCOURAGE YOUR HUSBAND TO DO THE SAME so he knows you're not the bad guy (if he hears anything of the sort, he should be able to think for himself and say "you're wrong, my wife is actually a saint to my mother"), send her gifts, NEVER EVER agree with anything negative anyone says about her, etc.
Lets say you have a friend who hates another mutual acquaintance you havent had the opportunity of knowing. Your friend simply cannot stand this 3rd party and tells you how horrible of a person she is night and day. But when you meet this 3rd party...she is so sweet to you...you end up thinking your friend must have lost her marbles. Thats the idea here. Complaining to your husband or MIL will accomplish zilch and give your more grief and drama then you can handle!!! So dont. Be the best you can be to her face and in front of others so people automatically think she is a nut. Thats it. Your job here is done.