How to avoid repeating "her" three times in one short sentence?

Habib’s talent reminds her family of her late grandmother on her father’s side.

It seems like I shouldn't remove any yet it doesn't look good this way.

If the OP must say that Habid's late grandmother is on her father's side they could shorten the sentence to

Habid's family said/say her talent reminded/reminds them of her father's late mother

May I say I approve of your ... instinct? - to look for ways of reducing duplicated words too close together. That is one of the subtle ways careful writers can enhance their readers' enjoyment. Seeking ways of expressing exactly the same meaning in fewer words is another. Variety in sentence lengths too. These all help to keep readers interested, or at least awake. There is no reason formal writing cannot employ a bit of literary style and flair.

I find reducing duplications of pronouns and articles to be least important. They serve essential grammatical functions and duplications must often just be accepted. I would not sacrifice a natural way of expressing an idea just to reduce duplicates of those parts of speech. I consider eliminating duplicated prepositions more important and the other parts of speech very important.

Regarding your sentence, it sounds to me like the natural way to express that idea. The duplicated uses of 'her' do not sound jarring.

The thing I'd consider is a comma before "on her father's side." That sort of removes one of them from the main body of the sentence, it becomes a parenthetic aside, just an extra bit of detail someone adds as an afterthought.