In what the government would do next

"Joanna Cherry, an SNP frontbench MP, said her party’s 35 MPs would support Benn’s “excellent” amendment, which rejects both May’s deal and a no-deal Brexit and gives parliament a say in what the government would do next."

(The Guardian.)

in what the government would do next - a prepositional phrase (a form); an adjunct (a function) where:

in - a preposition, the head of the PP phrase;

what the government would do next - a clause (an indirect question); a complement (in the PP) where:

what - a pronoun; a direct object [do what];

the - a determiner; the modifier in the NP [the government];

government - a noun; the subject in the clause [what the government would do next];

would - a modal verb (an auxiliary)

do - a predicator (the main verb);

next - an adverb (a form), an adjunct (a function [in the clause what the government would do next]).

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Is my analysis of the PP in what the government would do next acceptable?

Can what the government would do next be described as a clause embedded in the PP in what the government would do next?

Is [Benn’s “excellent” amendment] gives parliament a say a matrix clause in the independent (main) clause [Benn’s “excellent” amendment] gives parliament a say in what the government would do next?