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 ?