Kaizen is right. In the law we have two principles. One is yes, we like written contracts. The other is that if someone is silent where there is a duty to speak certain presumptions can be made. At the very least document it with a kind and business-like email, only on the one topic (if you ever have to introduce it in court you don't want to deal with all the other garbage that could be in there).
Dear Wife,
Thank you for our discussion of ________ in which we agreed that I will be going to stay with my parents for 6 weeks to give some time for us to each have space and for me to able to make some additional money. As we discussed, I will be returning to the house at the end of the 6 weeks. I hope this will give us both some time to work on ourselves and reflect on our situation.
You can be less formal if you want, but you get the gist.
