"å pleie" is interesting. Looking at a dictionary, the main meaning seems to be "to nurse" or "to tend" in the nursing sense e.g. "to tend a wound" (this also comes through in e.g. "hjelpepleier"). However it also appears to mean "to tend" in the frequency / habit sense as in this sentence i.e. "She tends to be at home".
Because of the English homonyms it is difficult to confirm whether this double meaning is indeed applicable or not and so I would be grateful if someone could help me out with this.
No, you can't translate this as "used to be". Here "pleier" is present tense, while "used to be" is past tense. If the sentence was "Hun pleide å være..." (past tense), that would be closer to "She used to be". Although maybe it's even closer to "She tended to be" or "She usually was". But note that the English phrase "she used to be" doesn't always carry the concept of "usually". It might just means "she formerly was", and not necessarily imply that it was "usual". For example, if I'm looking for my pencil, and I look on the table and say "It used to be here", I only mean that at some point in the past it was there. I don't mean that the pencil is usually there.
Just to be sure I understand this: Pleier is a verb, right? And "usually" is an adverb, so they aren't really equivalent. I'd think that "she is usually" is better translated as "hun er vanligvis"; these both use present tense (is/er) followed by an adverb (usually/vanligvis). And neither uses an infinitive. On the other hand, "hun pleier å være" is more exactly "she tends to be"; these both use a verb (pleier/tends) followed by an infinitive (å være/to be).
By "this", I assume you mean "pleier", so no, it's not a synonym of "vanligvis". The word "vanligvis" (meaning: "usually") is an adverb, while "å pleie" (meaning: "to tend") is a verb. This difference alone means they are not interchangeable. A literal word-for-word translation here would be "She tends to be at home". The translation here of "She usually is at home" can be thought of as perhaps a more "natural-sounding" way to say it in English. To use "vanligvis", you have to use it as an adverb, so you could say "Hun er vanligvis hjemme" (which is the literal word-for-word translation of "She is usually at home").
I'm a bit late to the party, but that would be the translation of:
"Hun pleier vanligvis å være hjemme."
"Vanligvis pleier hun å være hjemme."
Both technically redundant (as Luke pointed out), since what you tend to do and what you usually do would be the same, but not all that uncommon to hear.