I don't usually try to answer a story-identification question if I don't remember reading what might have been the same story, but in this case I decided to make an exception when I saw you mention the possibility that it might be something hosted on the Baen website. I figured it would only take a couple of minutes to check that idea.
So I Googled to search the www.baen.com website for certain words and phrases which might logically occur in a story such as you described . . . and darned if I didn't find something that looks like a pretty good match!
Her Brother's Keeper, by Mike Kupari. (Clicking on the title will take you directly to Chapter 1 on the Baen site.)
I read the first chapter, and glanced through some others. Not quite a perfect match for all the points you thought you remembered, but I believe it is still a very good match; too close for coincidence. I'll list some points:
Homeworld possibly named New Aberdeen/New Hebrides (something with
Scottish cultural overtones)
The first words in Chapter 1, after "Chapter 1," are establishing the setting of this opening scene:
Aberdeen Province, Northern Hemisphere
And when the heroine's father first speaks in this scene, his voice is described this way:
“My dear Catherine,” he said, still speaking with the ancient,
prespace Scottish accent that Avalon was known for.
Main character is a woman raised in privilege, who bucked social norms
by going to military college. (First woman in her homeworld's history,
and they changed the laws after she was gone to make sure she was the
In the course of this conversation, it becomes clear that Catherine Blackwood, the viewpoint character, did in fact rebel against Avalon's conventions for gender roles by pursuing a military career, although she was not literally the first, last, and only woman from Avalon to wear a military uniform. For instance:
“I was hardly the first Avalonian woman to serve on a military
“Indeed you weren’t, but you were the only female officer in living
memory serving not in the Women’s Auxiliary but in the actual armed
On the other hand, regarding your memory that the rules had been changed after she went to the Academy to join the Space Forces:
Before Catherine could complete her midshipman cruise on a Space
Forces ship, the Avalonian High Council rescinded a ruling that
allowed women to serve on board combat vessels. That ruling had been a
desperate wartime expedient dating back over a hundred years, to the
Second Interstellar War, but it had never been reversed.
Limited contact with her (wealthy) father, she has since come to
command a mercenary company on a small starship.
Catherine Blackwood commands a ship called the Andromeda. Various references in this scene make it clear that it is not owned by a military force; it is owned and commanded by Catherine Blackwood personally, and it takes on a series of contracts for various services. Delivering passengers and cargo, for instance; but Catherine also states that the ship has "nine confirmed pirate kills." Nobody tells us exactly how fast it can move across a span of light-years, but it clearly has FTL capability (something else you mentioned).
Main character's father calls her home. Instead of the argument that
she expects, he asks to hire her company's services. Her brother has
disappeared/been kidnapped on an expedition to some
back-end-of-nowhere planet (Archaeology?) and Daddy wants someone he
can trust to run the search/negotiations.
As Chapter 1 ends, Catherine's father is finally starting to explain why he sent for her. Cecil (apparently her only living sibling) is being held for ransom on another world (called Zanzibar). In Chapters 6 and 8 (8 is the last one that's available for free on the Baen website), we see Cecil's viewpoint, and yes, it appears that he and a friend are being treated as slave labor (well-fed and so forth, but not allowed to leave) in an archaeological dig. The villain is eager to get his hands on "alien artifacts" which he can then sell for large sums.
Meanwhile, a sheriff on a wild-west-ish planet engages in a gunfight
with persons (at least one of which is a cyborg) attempting to knock
off the local shipping terminal. He wins, but decides that he needs to
get out of the underfunded-lawman business. He answers an ad on the
local net, and sets an appointment with the commander of a merc
company that has landed to do some trading... And there the sample
Chapter 2 is set on the world of New Austin in the Lone Star system. It introduces us to a lawman called "Colonial Marshal Marcus Winchester." With some help from local deputy sheriffs, he wins a fight with a gang of outlaws led by a cyborg.
All things considered, I'm about 99.9 percent certain that this is the same material you remembered reading. However, as near as I can tell from Mike Kupari's Bibliography on ISFDB, this novel currently stands alone, instead of being part of a series of published works. (Whether or not sequels are planned for the future is something I wouldn't know.) But it says Kupari has also co-written a series of books with Larry Correia.