Allha ki tarf sa azshmish

Allah SWT test those whom he loves but where lies the difference between Allah's test and his "Azmaish".
And what is Azmaish in Islam?
Considering an example of a sister whose life was spend in hardships, problems from in-laws, her husband abandoning her and married someone else? And yet she remains devoted to him and her children?
How should one see it? As his test or "Allah ki narazgi?"

JazakAllah....