You're right yeah, although they tried to keep them (the right-wing populists) out for as long as possible, but - on the other hand - the coalition also has moderates and liberals, so it's bit of a mix really. But that presents another problem which was expressed by Brecht in that little poem:
After the uprising of the 17th June
The Secretary of the Writers Union
Had leaflets distributed in the Stalinallee
Stating that the people
Had forfeited the confidence of the government
And could win it back only
By redoubled efforts. Would it not be easier
In that case for the government
To dissolve the people
And elect another?
So people give majority of their votes, or at least a large percentage, to right-wing populist parties; and I'm quite sure that it will only intensify, so what's the solution? Liberal dictatorship, liberal one party state? There was actually a talk in Germany of banning AFD, now pretty much the most popular party in the country, at least in the East. Seems kind of crazy.
Of course, another solution would be to defang the right wing parties by adressing some of the issues that push people to vote for them, and that's what it think is happening. It's a tactic not a strategy really.