The sentence as written is ambiguous indeed and a bit weird since in tasca would in most cases be more idiomatic.
What is the source of this sentence? Context, as always, is all.
Having to guess as to its meaning, more likely phrasings could be:
Volete che mettano le mani in tasca?
(to ask in a general way about them having to put their hands in their own pockets), or
Volete che ci mettano le mani in tasca?
This would mean “in our pockets” and would mostly sound as a rhetorical question: “by any chance, should they steal from us?”
The sentence as literally given (Volete che mettano le mani nelle tasche?) more or less sounds as if there are some neutral pockets (neither ours nor theirs) here around and we are asking about what to do with them.