It has nothing to do with CF or spending time alone or whatever. I don't know you or your relationship so I can't speculate what works for you, but I can tell you how my relationship works... starting with money.
My wife and I make very different amounts of money. She makes about half what I make. Each pay check we each get the same exact dollar amount into our individual checking accounts and the rest goes into a joint checking account out of which we pay the mortgage and other stuff.
Everyone criticized us at the beginning of our relationship but we've found this works SOO well for us and we never have to get caught up in the petty fights we see our friends have about money. My wife doesn't grief me when I buy some geek toy and I don't grief her about pedicures or whatever. When there's extra money in the joint account we have a family meeting and decide whatever we're going to do with that extra money.
That core mentality in our relationships where we respect each others' individuality and have immense trust that we will each take care not to disrupt the common good. We each have our own computer, we go and do things with friends without having to bring spouses along.
We also do tons of things together. If your wife/significant other is griefing you about mild stuff then the problem is probably something else. She obviously feels insecure about your relationship. I would suggest improving the quality of time you spend together. It's so easy to get into the daily grind and basically ignore your significant other when you get home. Make a point to make a positive connection, have some cuddle time or whatever she's into to make sure she knows you care. Then she'll probably have less of a problem when you decide you want to play some game she doesn't give a crap about.