If there was no issue about taking in your MIL, how would you feel about her sending the necklace?
I agree that your instincts are probably right about her though.
What kind of person blocks out family members simply for a disagreement? It’s a person who doesn’t truly care about you. I’ve had to do a lot of soul searching about this, as I’ve had it happen within my own family. There are factors of pride, narcissistic qualities, triggered traumatic wounds misdirected, many factors. But the simple answer is they don’t care or they would have tried to make amends.
Sending the necklace may have been her way to try to make amends. But, as you suspect ulterior motives concerning you having to take in your MIL, maybe she was not sincere.
You could try to have a civil conversation with her to figure it out and try to put this relationship on the right track, but I don’t know if that will go very well. I had no luck with it. Does it hurt to try? Can it make anything worse? Do you care to try? Do you really care that much about each other?
The issue of taking in your MIL is a separate issue you will have to deal with anyway. (I have that issue, too

)