You might be overloaded with too many burdens and this can be a normal reaction to hyper-stress.
Maybe you are trying to tell your wife that you need some time off, some free time. A week-end will do, maybe. And then, in time, try to get another free week-end.

If she is not experiencing your stress, she can feel rejected, like you don't want to be with her and the baby. Tell her honestly that you adore her and the baby, but you just need some time off. Just sleeping or walking, just letting your mind wonder. Tell her that you will be happy to reciprocate the favor and one week-end she'll be out the her friends, going for massages or whatever and you'll take care of the baby and the house.

Having some time off, just to ourselves, is natural and really adds to our general health. If she is too scared to let you go for 2 days, then start some counseling, before these issues become too big.
In the while, if wife is not collaborating, pretend you are sick and that you cannot go back home for that weekend.
Is this cheating? If you don't save yourself, who will?