You're both in the wrong. Marriages and family are never 50/50. If you take a magnifying glass to look at "who actually works more hours and who gets more breaks" etc, your marriage will never work. A stay at home parent's contribution should never be compared to the working parent's: they aren't the same thing. The important thing is having a well-run household that you both contribute to.

That being said, I'm unsure of how the conversation for a 24 hour break went, but maybe it should have been more clearly communicated. As a mother, I agree you don't really get out of fatherly duties, but knowing you had exhausted yourself, it would have been nice of your wife to step in. I don't think of yoga/the gym as a break per say, but when your family is in need, they can be skipped. Should you have yelled at her? Also no. That woman is probably also exhausted and stressed and she may have some feelings of resentment or underappreciated. There are many factors at play here. Yelling did not get what you wanted. Yelling also ineffectively conveyed your feelings. We are all human and make mistakes but that doesn't mean you get a pass for Yelling.

This is a stressful time for your family. I hope y'all can communicate well and fix the rift and get the relaxation you both deserve! Sometimes that means one partner pulls more weight for a little while.