Elizabeth Barrett Browning was a contemporary of Jane Austen, though Austen was around 30 years older. Her relationship with Robert Browning is a famous real life romance, and sparked a great deal of literary output from both. The relationship is relevant to your inquiry because the relationship was disapproved of to a degree socially, at least by her family, so they carried out their courtship in secret, marrying "for love" as you state in your post. Read Aurora Leigh for an example of the literature inspired by their relationship. Below is an excerpt from EBB's Sonnets from the Portuguese that is quite romantic:

...

...

Yes, call me by my pet-name! let me hear

The name I used to run at, when a child,

From innocent play, and leave the cow-slips piled,

To glance up in some face that proved me dear

With the look of its eyes. I miss the clear

Fond voices which, being drawn and reconciled

Into the music of Heaven's undefiled,

Call me no longer. Silence on the bier,

While I call God—call God!—So let thy mouth

Be heir to those who are now exanimate.

Gather the north flowers to complete the south,

And catch the early love up in the late.

Yes, call me by that name,—and I, in truth,

With the same heart, will answer and not wait.

Are you including Jane Austen's works under stories about "women who had to marry men for money etc but where never truly happy"?

Do you mean books written at the time Jane Austen lived, or books written about the time that Jane Austen lived? A 20th century writer who wrote books focused on the British marriage market covering the same period that Jane Austen lived would be Georgette Heyer. Fiction books covering that period are generally referred to as Regency Romance.