This may work out for you, but I would never, ever let my kids spend 1 week (let alone 2 or more) with my sisters, SILs or BIL. Just won't happen ever. Not that I don't trust them, I just truly don't see a need for that. A sleepover one night? Fine. A weekend is okay too. But a week is unnecessary. I wouldn't even send my kids to my mom's or MIL's for a week. Not that I think they wouldn't be cared for, I know they will, but I just think it's too long. Now, if they're teens and my mom wants to take 1 of them on a special trip, I would likely agree to that. But just to sit at her home for a week, why?
I would most definitely want my family (or my husband's family for that matter) to stay in contact with our kids should something happen to one of us, but that can be accomplished without 2 week long visits. Why didn't the OP invite her BIL, new wife, and the niece to stay with them for a weekend? Or plan to meet up somewhere between them both to spend the day together? Why does it have to be 2 weeks alone with the niece?
It has everything to do with the amount of time. The longer a child stays at a relative the more a part of their family he or she becomes which helps form stronger bonds. You can't get to know someone on an overnight visit or even over a single weekend. Kids grow up and develop at such a fast rate of speed you need plenty of time to get to know them and see what kind of person they are growing up to be.
And there is no substitute for having them in person. Getting to know someone over the phone or computer doesn't make that person as real.
I just can't figure out what you are protecting them from. If the child gets homesick they can just come home early. If not, what is the worse that can happen? Stronger family bonds?