「[一応]{いちおう}」 would actually be a much more difficult word for a J-learner to use than a search in a dictionary might suggest. That is because, in informal speech, we use the word for meanings that are not listed in the dictionary.
Some years ago, I was hospitalized in Tokyo for a tonsillectomy. A day before my operation, my main doctor visited me in my room and introduced herself by saying:
「一応、私が[主治医]{しゅじい}の (last name) といいます。」 *主治医 = "doctor in charge"
「一応」, in this context, only meant "well", if I were to "translate" it. It was only a sign of humbleness on her part. None of the dictionary definitions would apply here: "tentatively", "roughly", "for the time being", "briefly", etc.
「一応、私の日本人妻の親と同居しています。」
is not such a bad sentence, especially if the reason for that living arrangement has already been explained prior to this sentence. It would have been better if you had said 「今は一応」 after a brief explanation of your reason instead of just 「一応」.
If you had described your living arrangement ONLY with this sentence, however, then using a more concrete expression like 「[一時的]{いちじてき}に」 would have been more desirable than using a vague word like 「一応」.