I have thought long and hard about how to reply to your post. As a mother of sons I can only tell you what it was like for me when my DS married. Marriage is a huge step in life. It signifies not only adulthood but the willingness to assume the responsibilities for not only your own life but also the life and happiness of your spouse and any possible offspring. It signifies flying out of the nest and no longer holding onto the edge and flapping your wings without risking that jump. When my DS took that leap he no longer wanted my advice or counsel. I was suddenly locked out of my DS's life. He had to prove himself to the world and he could not do that by running home to Mommy for help. I went from the inside to the outside of his life in very short order and it hurt like heck.
You can go back in my posts and find out how I thrashed around and how unfair I thought it all was. It was but that matters not at all. The truth is that my DS is married and what happens in his marriage is none of my business. It has taken years for me to come to terms with this reality and now I realize that this is the way things are actually supposed to be. I don't remember it all but the words "and forsaking all others, cleave only to him" used to be in the wedding ceremony and that was exactly what my DS was doing. I had to adjust to being an outsider in his life, oh well.
As I understand it daughters do not necessarily have the same reaction to the vows as sons do but I would be willing to bet that what you are interpreting as "jealousy" is actually your SIL reacting to what he believes is you interfering in his marriage. It would probably benefit you to approach the problem from a different point of view.
Perhaps someone else will chime in and give an opinion?