"Wild twists" is right.  I didn't expect half of the plot twists in this
one.

One thing, though.  I'm not sure what your intent was in this story.  You
seemed to be building it up as a gut-wrenching, emotional roller-coaster
(your title, among other things).  I suspect that was deliberately
misleading on your part, since it's not.  It's a fun read, but didn't really
grip me by my emotions and squeeze them.  If you really intended it to, the
Ranma/Sanko to Akane confrontation needs a lot more honing, plus you
probably have to cut the plot twists and jokes from that section of the
story.  If you really want that, it should be achievable; you have the raw
materials.  As it is, there was nothing here that would justify Akane's
calling it "the biggest mistake of my life" as she did in episode 14 (of
course, you've shown that the Matriarch Akane can be quite disingenuous in
her narration).

Anyway, details:

having them available for the wedding two weeks ago helped that much.

Weddings in Japan are fairly expensive affairs (usually).  Most fanfic
writers who deal in multiple failed weddings leave a lot more time
between than two weeks.  I don't think I'd change the time, though;
I think I'd suggest a side comment about this one being on the cheap.
Then again, that's kind of implicit anyway.

It's my child and I am not so dishonorable as my pop that I would
abandon my child!"

Grammar problem (then again, it's Ranma speaking).  "not dishonorable
like my pop"?  "not as dishonorable as my pop"?  I'm not sure why,
other than the joke, Ranma even brings his father up here.  (Genma
never abandoned Ranma, only Ukyou, who was not Genma's child.)

Akane smiled. "Yes, that's what I've come to call that wedding.
You know... like a shotgun wedding when the bride is pregnant?"

Good clue that you never really meant this to be "the Storm".

"Have you've seen Akane, Mom?"

Another instance of bad grammar.  "Have you seen Akane, Mom?"

     "Shampoo... it's an English word for hair soap." I gulped,

and it's the Japanese word for hair soap (spelled [in Romaji] "shanpuu"), so
your joke doesn't really work.

General:  I'm just not sure the whole premise of the story really works for
me.  The rest of Akane's family is there, as are the Saotomes and Dr. Tofu,
and NOBODY counsels Akane against marrying just Ranko?  Nobody other than
Dr. Tofu knew that anybody was pregnant, so why does everybody else just
accept the need for a quick marriage?  It seems that Akane, on her own,
decided on the need for a quick wedding to Ranko alone, without explanation,
and EVERYBODY just went along with it.  Unless she's paying for the wedding
herself, there's a credibility problem here.  And does it never occur to her
to change her mind, even during the ceremony?  Nobody suggests she marry all
three, and then "suspend" two of the three until the baby is born?  The
living arrangements are already those of a three-way marriage; what does
Akane expect to change?

I think you _could_ overcome most of this just by multiplying Akane's anger,
but I'm not sure that is in accord with where you're going.  Ranma/Sanko put
their feet in their mouths when Akane springs her plan; they all start
screaming at each other; a furious (almost Bitter End) Akane intimidates
everyone other than Ranma and Sanko into the quick wedding.  Akane's
collapse from anger suggests you had something like this in mind at one
point, but it misfires; it's too late, _after_ Ranma and Sanko have calmed
down.  You _could_ do this, but I think I'd actually like the story less, as
I'd like the characters less.  It's a problem.

The additional hints that this is a horrendous mistake begin to be taken as
crying wolf, at this point.  You can only get away with such hints so many
times without having a wolf appear before your readers:  1)  stop believing
you, and 2) get annoyed that you continue to cry wolf.