Is it fair to say that in A Doll's House the women strive to find happiness in two different ways?
Yes, it would be fair to say that the search for happiness is different, because the characters come from very different places in their life.
Nora, for example, strives to find happiness through acceptance: She sacrificed her time taking care of her Dad, and then sacrifice her dignity to take care of her husband.
Both cases ended up as failures: Her father died putting her in Torvald's hands, and Torvald placed more value on social stigma than on Nora's efforts to help him get back to health.
After this, Nora simply gave up and tried to find happiness through contemplation and not through the acceptance of others.
If we take Linde as an example of women striving for happiness, it would be strange to place her. She does not seem to be looking for happiness, but for the basic elements of survival: Company, a little comfort, and a reason to get up in the mornings (a job).
She has had a life of sacrifice and she has equally come out with nothing to show for it. When she saw Krogstaad, she saw in him the companion that she longed for.
There is very little romance in the play as a whole. There is no specific mention of the joys of love and marriage. Yet, there is a lot of talk of the convenience of marriage, which is a completely different story.
In a way, you could say that the women did try to find a form of happiness in completely different ways, but that none of those forms of happiness came in the shape of romance, nor fantasy: They were seeking basically for ways to cope with harsh realities.