Neither sentence is grammatically correct.
Because "hairband" is singular, both sentences need a determiner before "hairband". Perhaps it is "a hairband", or "her hairband", or "your hairband", or "the blue hairband"?
Each sentence combines two ideas.
One idea is that "Rina was sitting under a chair." This sentence is in the past progressive tense. It implies that Rina is probably not still under the chair.
The other idea is less clear. Do you mean:
a. "Rina was wearing a hairband" while she was under the chair, in the past progressive tense?
b. "Rina is wearing a hairband" now, in the present tense?
c. "Rina was wearing a hairband" while she was under the chair, and continues to wear the same hairband?
If you mean (a), you can use a parallel construction. This is natural in American English. For example:
Rina was sitting under a chair and wearing a hairband.
Rina was sitting under a chair while wearing a hairband.
Rina was wearing a hairband while sitting under a chair.
You could instead combine the ideas using a subordinate clause. For example:
Rina, who was wearing a hairband, was sitting under a chair.
If you mean (b), it is harder to use a parallel construction, because the tenses are different. But you can still express both ideas using a subordinate clause. For example:
Rina, who is wearing a hairband, was sitting under a chair.
Rina, who is now wearing a hairband, was sitting under a chair.
If you mean (b), you can convert the subordinate clause into a parenthetical note. For example:
Rina (the one wearing a hairband), was sitting under a chair.
Rina (the one now wearing a hairband), was sitting under a chair.
The word "now" makes it clearer that the two parts of the sentence have different tenses. It also implies that Rina was not wearing the hairband while sitting under the chair.
If you mean (c), I am not sure how to structure the sentence to combine the two ideas, plus the idea that Rina is still wearing the same hairband.
Sometimes the word "now" does not indicate present tense. For example, you could tell a story like this:
Rina had a bad day yesterday.
She put on her favorite hairband in the morning. As she was walking to school, a tree fell down in front of her. Her hairband fell off. It almost broke!
She managed to catch it. She was so scared that she needed to take a few minutes to gather her wits. She put her hairband back on, and continued on her way.
Rina was three minutes late getting to school. The teacher punished Rina for being late. The teacher told her to sit under a chair for five minutes!
So Rina, now wearing her hairband, was sitting under a chair. That's when she saw the weird marks on the floor.
In this story, "now" refers to the time when "Rina was sitting under a chair."