You’ve literally listed day to day life for the vast majority of immigrant parents in any country. It is difficult to learn to use a new language, and it is not possible for adults to attain native speaker fluency, despite it being pitched as some kind of benchmark against which to measure people. It is difficult to find a social network. It is difficult to understand and navigate school systems for your kids.
You've explained that you agree with what you called failed integration, and it’s really courageous of you to disclose that a family member of yours has contributed to the failure you see. It’s good to see that you’ve not been lured by the old ‘we’re not immigrants we’re expats’ rhetoric 👏
But you seem to be suggesting that she has tried, implying that others haven’t? How do you know they haven’t? What do you mean by ‘not doing ones best to adapt?’
If you mean not learning the language, not having a German social network etc, then have you considered some of the structural reasons why it may be harder for some people to do those things than it is for others? Can you think of anything which German society could do to lessen those barriers?
You yourself said that immigration works both ways, well, it doesn’t, but integration tends to be a multi-party process, I guess that’s what you meant. It is not enough for a host country to put in place things like education etc, they also have to show that they treat immigrants with dignity and respect on a day to day basis.
A huge part of the problem in Germany and other European countries is the downright xenophobic refusal of normal everyday people to do that.