that test named "Delfin4", it's a ridiculous one, was just introduced and NRW is the only state were it's compulsory.
It's only in German, and kids are required to repeat phantasy words and must exactly provide the results they expect or points are subtracted.
Many German native speaker children fail (!!!!), but that's not an administrative problem, because the extra training is provided at the nursery school the children attend. Or if your children don't, they would get the extra speech/language tution for free at the nursery school, or at the speech therapist if you decline the nursery school option (which they would try to convince you).
It's especially designed to identify children of immigrants who are not enrolled in nursery programms yet, to to integrate them to the schooling system and prepare them for elementary school. And of course to identify German native-speaking children with language gaps.
This in itself is contradictory, because the children get there yearly medical check-ups (which are by the way compulsory too, since last year), and the pediatricians should be able to see language problems and make a referral.
Or the nursery workers would recommend to see a pediatrician, as most children are technically enrolled in nursery school programmes.
There are several online/distance courses from the UK and the US, also $$, there are cheaper French distance programmes, should you speak French.
You can't escape their "invitation", it's done via the Einwohnermeldeamt, and you get it automatically.
Normally the bureaucrats consider up to two years a temporary residence, but it depends how you present your case to them. If you are native English speaker and you are just a short while in Germany or if you plan to send your children to an $$$ International School later on, it would be logic to me, that you should get an exemption for the language test. Do you have other expat friends who encountered this problem yet?
Here is the official descriptionhttps://www.schulministerium.nrw.de/...ied/index.html
And here are some critical reviews of the test (on public tv)http://www.wdr.de/themen/wissen/bild...n4/index.jhtml
Hope you don't have to participate!