I'm a stay-at-home mom of a 16-month old. I put my daughter in daycare for two days during the week. She seems to be getting a lot out of it and I think she's happy. I use those two days to get groceries, clean the house, and to get some time alone. My husband thinks it's great, but I have a few family members who don't really don't like that I use daycare when I don't have an "outside" job.
It's interesting that anyone would take issue with a stay-at-home mother taking time off. I suppose it appears to contradict the stay-at-home part of it.
Curiously, though, no one refers to a father in the workforce as a "working father," nor do they think his time off contradicts his status as a "working man." Additionally, no one takes issue with anyone putting in just 40 hours a week and, in some cases, getting paid more per hour for putting in more than 40 hours.
Most jobs (like your husband's and perhaps those of your family members) give a person two days off and don't require a person to be at work 24 hours a day the other five days of the week. Most people get to go home at the end of the day and not return to their work until the next day.
With this in mind, consider giving it to your family members in mathematical terms:
Let’s assume you’re putting your child in daycare for eight hours. If you take two days off, you’re on duty the other five days for the entirety of those days. When you include the time the child is home on the days he/she goes to daycare, your two days off still has you putting in a 152-hour workweek. Even if you took three days off, you’re putting in a 144-hour workweek.
In the workforce, a day off means putting in zero hours. On your days off, you're still putting in 16 hours, not including the time you used to get groceries and clean. I'm tired just calculating those kinds of hours.
Having raised three children from birth to college, I can attest to the importance of time off for stay-at-home moms. I can further attest to the importance of something most young stay-at-home moms are never told: the most valuable and effective stay-at-home time is not when the children are young, but rather when they get to be about age 12.
Pre-teens and young teenagers are especially in need of readily available adult supervision, guidance, love, and support. This age group is in a state of physiological change matched only by their first two years of life.
Use the time now to get to know your child, to instill your rules, values, and standards, and to make the most of your time. Take those regular days off now to replenish yourself. You're going to need that energy later when the messes are bigger, the tantrums are louder, and the needs are greater.