I was going in the direction of "this is not a big deal" until the end when you said she was going to go 30 miles from home just to have her child in the same school as yours. What was some pretty garden-variety jealousy and copycatting on her part has turned weird, to me. But you can do nothing about it.
Repeat that about a million times: "I can do nothing about it. And right now, this second in time, this day, no one on the planet is worrying about this but ME. And I choose not to burn up my precious mental energy on this person."
Then you have to make that reality. Stop eating yourself up over her. It is entirely possible that she copies you because she admires you, craves your life in every way, and thinks it is the highest form of flattery to imitate someone else (some would say it is indeed flattery). So: Tell yourself -- and you won't believe it at first but keep saying it -- to put the best spin on this you can. She is living her life and you are living yours; you are at similar ages and stages in your lives so of course you both have kids, houses, cars, school choices at the same time. Hers happen to coincide with yours in ways that make you uncomfortable but you CAN choose to stop keeping tabs of each thing she does that mimics you. You can choose to have less contact with her and her family. You can choose to be too busy to have your kids and hers get together more than you want, if she pushes for play dates etc. You. Can. Choose.
As your kids get older this can get worse or it can get better. Help the situation to get better. Your son and hers are totally different personalities, you say; so rest assured that as they get older, they are going to be into different activities. Will she really shove her academic kid into some activity that your more outgoing son prefers, or vice versa? The boys are also far enough apart in age that they should not be in the same grade at school and eventually, as activities are based more on age and grade, they likely will not be in the same activities.
If she tries to keep scheduling everything together (like the swimming lessons), you have to get strong enough to say out loud and at the very start: "SIL, I know you think it would be great for X to join Y's Cub Scout troop but I think it would be best if they each were in different troops." You don't owe an explanation. Do the same with other activities. If you must tell her something, tell her that since they are cousins and close in age, you want them to develop their own space and activities. The one-year difference in school years will begin to help you with this as they get older, too -- your older child will want to hang with his friends, not with his cousin who's in the next grade down. Go with that. And you CAN tell school administrators or teachers that you do not want the boys in programs together; you can tell scout leaders or others that you prefer the cousins not be in the same troop, group, etc.
Be too busy. If she is in your face with play dates for the cousins, or (heaven forbid) starts wanting all of you to vacation together as one big happy family, be too busy and learn to say no. Sign your kid up for classes and don't tell her -- why does she need to know your son is doing swimming on day X at time Y? She doesn't need to know that you signed your son up for an art camp in the summer for a week at the rec center, or for a soccer clinic with his buddy from preschool. Keep those things to yourself. If she asks, tell her -- several weeks into the camp or clinic. If she's nosy about all his activities, a polite but cool "We're looking at a lot of possibilities with some of his friends from school" is fine.
You do not ever once mention your husband's attitude toward his sister and her actions over the years. It is very telling that the entire post does not say if he also has your resentments toward her or if he even feels that she's intrusive or copying. I would bet maybe he doesn't; he's used to his sister doing what she wants and he doesn't see her actions as the threat you seem to perceive. He might get more upset about it if he realized that she is going to compare your kids for life, but he also might know from experience to just let it roll off his back. Can you do the same?