What is a good word for the Exhale portion of a laugh?

I would suggest "spasmodic cackling" or perhaps "spasmodic laughter".

Consider chortle. It is a blend of chuckle and snort.

A joyful, somewhat muffled laugh, rather like a snorting chuckle. ^[Wiktionary]

Similarly, snort can be used, as in snorts of laughter.

What about something along the lines of diaphragmatic spasms? As in, spasms of the diaphragm.

Although none of the pure synonyms for the verb “exhale” seem to be limited to laughter, two of them, “puff” and “gust,” are found here as nouns on a list also containing “exhalation” (#8), and since “gust” already has an idiomatic connection with “laughter” (gust(s) of laughter), I think “gust/s” would work well enough in your particular example:

Smothering and terrified and still strangling on the tail-end of her breathless laughter in sharp lung-flattening gusts.