I have no idea at all why the OP is getting such a hard time. Unless the rest of you have children who play for long stretches independently at 12-14 months old, or you stick them in front of the telly all day?
I work three days a week and I'm at home for two. With an almost-three-year-old. It's easier, on my days at home, for me to run physical errands, do time-consuming tasks like laundry, and generally pick up after her than it is for DH/me to do those things after hours. It's easier on my days at work to make complicated phone calls, because I'm not having to fend off "mummy who are you talking to, who are you talking to mummy, can i talk, I want to do some snipping will you help me do some snipping WHO ARE YOU TALKING TO". If she were younger, I'd be having to worry about her getting into trouble, breaking things, falling over. The OP's toddler is very young, my memory is that they needed pretty much 100% vigilance at that age.
If I go out with her all day I can't do housework and long phone calls. If I stay in with her, I'm pretty much constantly entertaining her, picking up after her, helping her go for a wee, making a snack, cleaning up after the snack, etc. There isn't actually a break - I mean okay, I can sit down on the sofa and read her a book, or meet a friend for coffee in a playground while our children run around together, but in the sense of free time, autonomy, doing something that requires thatn more than half of my concentration is elsewhere than DD? Never. I'm not lazy. I don't open a book, I don't open the laptop, I don't turn on the television.
Why is everyone talking about the OP getting to go for a walk and have a coffee as if dragging a young toddler to the shops is the same as having a nice stroll on one's own? On my days in court, I make small talk with other lawyers while we're waiting for a judge, is that the same as "having a nice chat with friends", then? It's all context.