Grammar analysis: [We] [two brothers] are responsible for this act. [We] [both] are responsible for this act

[1] We two brothers are responsible for this act.

[2] We both are responsible for this act.

No, they are neither appositives nor complements.

In [1] "two brothers" functions as head of the subject NP "we two brothers" in which “we” is a personal determinative and "two brothers" is a nominal consisting of "brothers" as head and "two" as modifier.

In [2] “both” functions as a quantificational adjunct in clause structure. It is separable and not part of the subject NP, which is just the pronoun "we". That it's an adjunct can be seen from the fact that it is movable: we can have "We are both responsible for this act" with no change in meaning.

I will expand on the answer given by BillJ.

Your two examples

[1] i We two brothers are responsible for this act.
ii We both are responsible for this act.

cannot both be analyzed the same way.

In [1i], two brothers is the head of the noun phrase (NP) we two brothers. In that NP, we is a determinative rather than a pronoun. The NP functions as the subject of the sentence.

In [1ii], both is a quantificational adjunct that is part of the NP we both. That NP, which functions as the subject of the sentence, has the pronoun we as the head. However, both can be moved to the position between are and responsible (we are both responsible for this act) so that it is no longer part of the NP, although it remains semantically linked to it.

Discussion

One difference between [1i] and [1ii] is that only the latter remains acceptable if we is replaced by they:

^{(The asterisk, '*', signifies that what follows is not acceptable.)}

[2] i *They two brothers are responsible for this act.
ii They both are responsible for this act.

This shows that we in [1i] has a special function. According to CGEL (p. 374) the words we and you are sometimes not pronouns, but rather determinatives (and are thus called 'personal determinatives'). Here is almost the same sentence, but this time we is a pronoun:

[3] We, two brothers, are responsible for this act.

In [3], two brothers is a supplementary appositive of the pronoun we.

Here is CGEL's discussion in full.

7.2 The personal determinatives we_d and you_d

[5]  i  [We_d supporters of a federal Europe] will eventually win the argument.
      ii  [You_d students] should form a society.

We_d and You_d here are the determinative counterparts of the 1st and 2nd person plural pronouns we_p and you_p that we have in We_p will eventually win the argument and You_p should form a society. Like the demonstratives, we_d and you_d mark the NP [noun phrase] as definite, but this time what is expressed in addition to definiteness is person deixis: we denotes a set containing the speaker, you a set containing at least one addressee but not the speaker. We_d like the pronoun, inflects for case, with nominative we contrasting with accusative us; the distribution of these case-forms is described in §16.2.

It should be noted that the personal determinatives are exactly parallel to other definite determiners such as the demonstratives and the definite article in, for example, permitting the universal quantifier as a predeterminer. Compare:

[6]  i  a.  all we_d supporters of a federal Europe           b.  all you_d students
      ii  a.  all those supporters of a federal Europe        b.  all the students

This property distinguishes them from the personal pronouns, which permit all only when postmodified: All we/you who support a federal Europe will win the argument, but not *All we/you will win the argument.

In [7], however, we and you are pronouns:

[7]  i  We_p , the supporters of a federal Europe, will eventually win the argument.
      ii  You_p , the students, should form a society.

Here, the determiner of supporters and students is clearly the definite article, and the NPs formed with the definite article are full NPs in their own right which stand in supplementary apposition to the personal pronouns we and you (see Ch. 15, §5, for discussion of this construction). One reflection of this difference is that the personal determiners can only be the 1st person plural we and the 2nd person plural you, while all the personal pronouns regardless of person and number occur in the appositional construction. We illustrate this with the 1st person singular I, the 2nd person singular you, and the 3rd person plural they.

[8]                       DETERMINER + HEAD                                    APPOSITIONAL CONSTRUCTION
    i  a.  *I president declare the meeting open.      b.  I, the president, declare the meeting open.
   ii  a.  *You proponent of a federal Europe    b.  You, the proponent of a federal Europe,
              should support this proposal.                              should support this proposal.
  iii  a.  *They poets are our guides.                          b.  They, the poets, are our guides.

Another difference between [1i] and [1ii] concerns the effect of change in linear position. Consider

[3]  i  We two brothers are responsible for this act.
      ii  We are two brothers responsible for this act.
     iii  Two brothers responsible for this act are us.

What [3ii] and [3iii] show is that two brothers responsible for this act is a noun phrase (NP).

Now consider

[4]  i  We both are responsible for this act .
      ii  We are both responsible for this act.
     iii  *Both responsible for this act are us.

In this case, [4iii] is not acceptable, which shows that both responsible for this act is not an NP.

This is related to the fact that both belongs with words such as all and each in that they are all determinatives. According to CGEL (p. 102), when these determinations are positioned inside the NP (as in in [4i], then they belong to the subject both semantically and syntactically. But when they are positioned outside the NP (as in [4ii]), then they semantically belong with the subject, but function as quantificational adjuncts that can be positioned outside the NP. CGEL gives the following examples using all, but the same remarks apply to both. The reason I'm reproducing the following passage from CGEL is to show how flexible such adjuncts are with respect to linear position, and in particular the fact that they can be placed outside their 'native' NP:

Quantificational adjuncts

A comparable difference [to the case of adverbs] in position between auxiliaries and lexical verbs is found with certain determinatives, such as all, both, each (Ch. 5, § 9.2), that are semantically associated with the subject:

[36]                      LEXICAL VERB                                  AUXILIARY VERB
            i  a.  All the players took a card.      b.  All the players had taken a card.
           ii  a.  The players all took a card.     b.  The players all had taken a card.
          iii  a.  *The players took all a card.   b.  The players had all taken a card.

In the [i] versions all belongs syntactically and semantically in the subject: it functions within the NP all the players and it quantifies over players. Such items can be positioned outside the NP, and the [ii] versions show all in pre-verbal position. If the verb is an auxiliary, it can follow the verb, as in [iiib] - which is preferred over [iib]. But it cannot follow a lexical verb, as is evident from the ungrammaticality of [iiia].