I used to really be on the bandwagon for multi-lingual children (immersion schools, camps, summer breaks in foreign language camps). I even went to Concordia Language Village in Minnesota USA when I was younger to learn Spanish in total immersion, but.... I've since changed my mind. There is little to no benefit to being bi/multilingual anymore.
If you want your kids to speak a language due to cultural reasons, go for it, but I think that is probably a selfish move that will hinder their "normal" primary education (reading, writing, math, history, science, art, music). I would absolutely NOT move to another country just so my kids can learn a language for cultural reasons if you value their primary education. Technology will VERY soon be/already at a please with real-time translation making human translators and bi-lingual business negotiations obsolete. Some older people have a hard time believing this (same with self-driving cars, but that's a different rant), but your children will be able to pop in earbuds and speak to anyone in their current language, and the recipient will hear it in their language of choice in REAL TIME. Augmented reality (download Google Goggles on your phone) can already translate menus, street signs, or anything written in many phonecian based alphabets, some character languages, and they are working on adding more character languages soon. If you don't want to take pictures of the menu, just pop on a pair of augmented reality goggles and literally every written language will be translated into your language of choice IN REAL TIME. This is not a far off distant future. It will be here very soon, less than 10 years for sure (Google Glass was a bit bleeding edge, but it will be back in some variation).
There is simply no real/business-world reason to teach your children a foreign language whatsoever. I think parents who send their kids to these immersion schools are totally within their rights to do so, and they very well may value the cultural component of their education higher than their primary education, and i do not judge them for doing it. But, in my experience, they say, "Yes, little Timmy is in Chinese immersion school - being able to speak Chinese will open SO MANY doors for him when he's older." False. Do not send your kid to immersion school for this reason. It is a lie.
Also, heaven forbid you send your kid to an immersion school/move countries for like 3-5 years and no more. You might as well have just taken those 3 years, pulled your kids out of school and gone on vacation. They won't have a solid grasp on the immersion school language, and they will have fallen behind in the primary subjects as well. This has been well-studied, and is the truth. Immersion school students test worse than primary language schools up until something like grade 6 or 7. If you switch schools before they make up that gap, you kid is going to be behind in school.
The one exception to this is if your children's primary language is not English, Chinese, Spanish, Hindi or Arabic. Then, I would encourage you to move so they learn one of these languages vs a small non-business language. However, by the sounds of it, you are covered in this area.
I hope I'm not coming across too agressively, i just feel really passionate about this topic. I don't want kids going to these immersion schools for any reason other than valuing cultural acceptance over primary education.