A. You never get a vacation day from parenthood. No matter how off-duty you are, the parent-child mind meld is always on call, the heartstrings firmly attached. But you do need a break from the physical job of parenting every now and then -- whether it's for an hour or a few -- and it's fine for a child to know that. Explain a simplified version of this so she understands you're not trying to get away from her.
I wouldn't be too concerned about her getting the wrong impression, either. Kids are oblivious to subtle subtext; they're not sitting around thinking, "Oh, I see, so Mommy and Daddy perceive their roles as parents not as a calling but as just another job...." All kids know is that their parents are at their 24-hour-a-day disposal and they just need to demand to receive.
As for her not bothering you when it's your day off at home, try to get out of the house for at least part of the day. It's weird to be there and yet not be there, and it's asking a lot to expect a toddler to exercise the level of self-control required not to ask for attention.
Between your turn-taking, it's a good idea to plan some family time into your weekends. Workweeks are so hectic for most of us that weekends are often the only time a kid gets to be with Mom and Dad at the same time, with neither parent rushing off or thinking about the job.