"Rest from <something>" is an idiomatic English phrase, however, it's probably not very common in this context.*
The more common way of phrasing this in contemporary American English would be: I need to take a break from my wife.
Note that this can sound quite strong. Taking a break from your spouse might imply the kind of trial separation that is often a precursor to a divorce. If an unmarried person suggests to their partner that they take a break, it's likely that they're thinking about breaking up.
In the right context, where it's clear that you're mildly frustrated and making a joke, taking a break from your wife could sound appropriate.
You might be safer using a different phrasing, which is careful to avoid suggesting something like divorce, such as, "My wife and I have been getting on each other's nerves. I need to take some more time for myself."
*For whatever reason (probably because of some common translation of the Bible), contemporary uses of the phrase "rest from <something>" appear most often in Christian literature:
"In that wonderful day when the Lord gives his people rest from sorrow and fear, from slavery and chains."
"It is a rest from dead works that cannot earn salvation (Heb. 6:1)."
"And, please note that Jesus promises rest from your weariness and burdens"