need advice on showing character personality

Hi and welcome to A2K!

One way is to think of her almost like a clichéd man, e. g. the strong and silent type. She might not be overly demonstrably affectionate, but she can show she cares by doing thoughtful things.

E. g. maybe she always fill the car with gas when she borrows it. Or she cleans the dishes without being asked. Or the laundry just magically appears, completely done, and the family figures out later that she was the one doing it.

It can also be wordlessly defusing situations, such as taking the niece out bowling (or whatever is appropriate within your universe) when the niece's parents are about to have a serious discussion, or seem to need some alone time.

What if the niece sees a dress (or an Xbox game or, as I said, whatever fits inside the world you've built) in a shop window and is saving for it or hoping to get it but suddenly it's gone? And then a few months later, for a birthday or Christmas or just because, there's an anonymous wrapped gift and there's the dress? Or she could even find it in your character's possessions, possibly by snooping or even wholly by accident, and it could be revealed that the dress was meant as a gift to be given later.

Portray your characters however you want. I like your plan and think you're off to a good start.

"The readers learn early in the story that she was abused but the character is more than that and struggles with showing her new 'family' that she cares about them even when she is known to lash out"

This might come across as nitpicking; I think it's important though:
in my view, people who have been abused and act angry don't have at heart to show they care. I'd expect them, on the contrary, to be genuinely convinced that any nice things they do are *not* because they care.

@jespah offered some very good ideas. Your challenge is to work out from whose perspective(s) they make it into the story. You seemed to imply it'd be from just the abuse victim's perspective.

The writer has his or her own pov.
Write your own story.

I may be known to lash out, but you can trust that in true fact I am actually struggling to show I care about your input there:
F*ck You!