"She usually wants to swim in the morning."
Translation:Hon brukar vilja simma på morgonen.
(att) vilja = (to) want (to)
(att) vilja att … = (to) want (that) …
in the first form, "vilja" acts as an auxiliary verb and requires another infinitive main verb (unless you are a toddler). the "to" of "want to" is automatically implied and has no separate swedish translation. you simply append the main verb in the infinite form (here: "(att) vilja simma", "(to) want to swim").
in the second form ("(att) vilja att …"), "vilja" acts as the main verb and the trailing "att …" introduces a subordinate clause that requires another subject and verb, but that was not duo's question and you missed to provide a subject for the subclause as well. "hon brukar vilja att simma" literally translates to "she usually wants that swim(ming)", which makes no sense.
"(att) bruka" is yet another auxiliary verb that requires an infinitive verb to follow (here: "(att) bruka vilja …", "(to) tend to wanting (to) …" or "(to) be used to wanting (to) …" or simply "(to) usually want (to) …"). because "(att) bruka" is the first verb in this train of verbs (i.e. in the predicate of the sentence, "(att) bruka vilja simma") it gets conjugated to "brukar".
I'm neither an English nor Swedish native speaker, but I try to explain (at least that's how I understand it): "brukar" it a verb, so you can't replace it with vanligen. It means something like: doing it usually So the sentecne is: She "usually does" to want to swim in the morning (And as "bruka" is one of the verbs that behave like modal auxiliaries, there's no "att" requiered)