During the 1950’s in segregated Louisiana, a working-class African American mother and wife struggles with unforeseen births, deaths and racial issues while pursuing an unconventional career.

What specifically does the mother need to achieve? A struggle is good and all but a logline needs to focus the reader's attention at one specific goal.
There's also no need to specify that she struggles with racial issues, that is very clear from the setting and period. Leveraging common knowledge, of this type, in a logline gives power to the premise as the reader puts the pieces together in their mind's eye without having the obvious spelled out.

As a rule, the word 'struggles' is bad for a logline. The word 'must' should replace it.

When her daughter unexpectedly gets pregnant, an African?American?in 1950's America must... (Then tell us what she must do)

As usual, I agree with Dkpough1.

I'm a little confused as to how a birth is unforeseen. I appreciate that there are occasions where it happens but in the majority of cases a woman would probably be aware of it.

When choosing a genre, in my opinion, it must be obvious where the humour, terror, romance, drama etc is coming from in a logline. I would very much expect a logline in the "romance" genre to hint at a love interest at the very least. If the romantic element of this story is merely a subplot perhaps consider putting this in drama instead.

I won't repeat what Dkpough has said about the inciting incident and the goal as he is spot on. However, I will say that, to me, dealing with births, deaths and racism is simply life for a black woman in 1950s Louisiana - "an African American woman struggles with life while pursuing an unconventional career." That's how I read this if it's simplified a bit. It's incredibly vague across the board. Is her career unconventional because she's black? Because she's a woman? Because she's an alligator wrestler? Specificity is the key to making sure that the reader understands what the story is about.

My advice is tell us what her profession is when you describe her (a black nurse), switch the genre to a drama, and give us a clear inciting incident and the corresponding goal.

Hope this helps.