And you are still claiming that the refugee crisis is not a problem in Germany or the EU
I wrote it is not the definining problem in Germany or the EU. The refugee crisis is not the reason why the youth organization of the SPD (which is the OP of this thread) is against a coalition with Merkel, they believe that the SPD has not received enough concessions in other areas. Neither is the refugee crisis currently the big talking point in Bruessels, that would be Brexit, Poland's justice reform and the proposals of Macron.
Look at the development in countries like Poland, Austria, Hungary or the Czech Republic.
Austria always had a significant leaning for the right-wing politicians, altough no doubt the pictures of 2015 helped (even though Merkel did them a huge favour by taking those refugees who were already in Austria). That being said we shall see how the new Austrian government will affect Europe, since Kurz explicately reserved the European policy for him and not his coalition partner.
Orban was already in power and well on his way to consolidate his position with xenophobic policies and we know that he actually asked Merkel in summer 2015 to take some of the refugees who came to Germany. And even then this issue might not be as important as he hoped, since he e.g. failed to motivate enough Hungarians to vote on a plebiscite against refugees some time ago. As for Poland, well I sincerely hope that the Polish were not gullible enough to vote for PiS because of this, (since refugees are hardly a relevant issue for Poland) and from what I have read and heard, promises like the money given to parents were more important for many voerts.
Remember how strong the right wingers in France, the Netherlands, Italy and Greece already are, and how many votes the AfD got in the last election.
All countries in which they failed to gain a majority, in fact Greece is currently ruled by socialists. And the AfD is still a small party in Germany and likely to suffer from infighting during the next few years, once they have to decide how openly xenophobic and antisemitic they want to be. It is already happening.
mostly failed to integrate non-European immigrants in the past,
This is an exaggeration. The majority of the immigrants are decently integrated, there are problems with parallel societies, but this only affects a minority of the immigrants. Of course, there is much room for improvement, but Germany did much better than e.g. France or Belgium overall.
How do you inculcate German values of secular education, non-sectarian government and social equality of the sexes to children whose parents find those values to be abhorrent?
Simple, get them into schools, provide them with language courses and make sure that they stay in school as long as possible. The main problem in the past was that the German school system mostly had children in the school only for half a day, but now children spend most of their time in school where they learn the language.