in English you usually can't put an adverb between a verb and its object, so you'd have to put it somewhere else
the only place that sounds natural is "we also want to visit Denmark", though "we want to also visit Denmark" and "we want to visit Denmark also" (you'd usually say "too" here instead) are not ungrammatical as far as I know
Different meanings. We also want to visit Denmark - someone else has already been there, and we also want to go. We want to also visit Denmark - in addition to passing by, really visit etc We want to visit also Denmark - visiting somewhere else, but here putting emphasis on also Denmark..