Hi Mom on the GO! The rule of etiquette is that a note expressing gratitude must be sent for any gift from which you were unable to express your gratitude in person. So, officially, yes.
However...I think the real answer depends on the protocol you (and your SIL) have used in the past. Have you always sent notes in the past? If so, I think you may want to continue for now -- especially since you and she are not speaking. (You don't want her to "read into" something that's not there!) If you haven't sent notes, would it look odd to suddenly send a note now? Are you looking for an opportunity to break the ice? If so, would a note be a good way to do so?
Once you and she are on good terms again, maybe you could ask "Hey -- what do you want to do about thank you notes? Should we have the kids write them, or skip it?" Usually, I'm a hard-core thank you note supporter. But I have a SIL who never does thank you notes. She specifically asked that we stop sending the notes. So, I have obliged and stopped the notes with this one part of the family.