"...the jury, including its two alternative members, is/are in
There are two issues with the above that have bearing on whether to use "is" or "are":
1. Is the phrase "including its two alternative members" part of the subject?
No, it is not.
The phrase "including its two alternatives" is merely a parenthetical phrase that nonrestrictively modifes the subject "jury."
For further reference, see the following link and review the point labeled "5":
Or see the follwing link and review what is labeled "Rule 5a":
To be clear, the only word that can enjoin an additional subject to a prior singular subject and make the subject count plural is "and." Phrases, like ones starting with "along with" and "including," cannot.
2. Is the subject "jury" singular or plural?
The word "jury" is a collective noun for "jurors" (i.e. "juror" in plural). When it comes to how collective nouns are counted, the rules are not black-and-white.
Generally speaking, British English (BrE) counts collective nouns as plural, while American English (AmE) counts collective nouns as singular. That means that in BrE, one would generally say:
"...the jury, including its two alternative members, are in
But in AmE, one would generally say:
"...the jury, including its two alternative members, is in
You'll notice I said "generally." It is not ungrammatical in BrE to say "is," nor is it ungrammatical in AmE to say "are." That's grammar, though, not style.
As regards style, if you are to follow a specific style guide (i.e., Hart's Rules, Chicago Manual of Style, MLA, APA, etc.), then it may dictate how you are to treat collective nouns, whether as singular or as plural, so you should consult that style guide. Otherwise, you can do what you like, my only caveat being this:
Except in a few special cases (e.g., the collective noun "police"), lay Americans tend to see using plural conjugations with collective nouns as ungrammatical, so you may be seen as such if you do so, like if you say "the jury are" to an American.
The converse is not true of lay Brits. While plural conjugation (e.g., "are") is more often used for collective nouns, singular conjugation (e.g., "is") isn't perceived as wrong but instead, if perceived as anything at all, is perceived as emphasizing the group acting as one, as a singularity, and deemphasizing their plurality.
Since the phrase "including its two alternative members" does not make a singular subject plural, the question of whether to use "is" or "are" falls to whether the collective noun "jury" is counted as singular or plural, respectively. Whether "jury" is counted as singular or plural as a subject for verb conjugation, generally speaking, depends on whether the English is American English or British English, respectively. In normal usage, if the English is American, then "jury" is all but invariably counted as singular, so you'd all but invariably use the singular conjugation "is," but if the English is British, then "jury" is typically counted as plural, so you'd typically use the plural conjugation "are."