"problematic relationship" is correct and can be used in written English.
Example: John and Sarah's problematic relationship finally ended in a bitter breakup.
This is inherently a problematic relationship.
And that was his problematic relationship with reality.
The problematic relationship between doctors and companies was also highlighted.
The EU has always had a problematic relationship with democracy.
And the problematic relationship between food and the body that features in her writing?
Kimmings is not an alcoholic, but she admits to a "problematic relationship" with alcohol.
"We have a problematic relationship with our own history, especially with art.
But the roots of this show lie in his problematic relationship with the piece.
San Francisco's Golden Gate Park exemplifies the state's problematic relationship with greened landscaped.
Addresses the problematic relationship between storytelling and games, from both an analytical and practical standpoint.
It must manage a problematic relationship with China, not to mention an unstable, nuclear-armed Pakistan.
