So many of your issues have familiar undertones in my marriage also.
Based on the story that you told of the picking the kids up, etc, my guess is that she has no idea of the impact of her behavior on you (even if you told her). Sounds like she’s turning a blind eye, not because she’s bad or doesn’t have feelings for you, but perhaps because she’s more aware of her own needs.
The part of your picking up your child from the play date can be as simple as her not being sure she’d get back in time. This might irk you that she did arrive on time in the end, but it seems more responsible to me that she expressed concern in advance about the possibility and made alternate arrangements. I’d sit down with her and clarify that your working from home has to be on condition that it’s without distractions, except in an emergency (and elaborate what that means: she’s at the doctor, kid’s school calls and says kid’s vomiting(c’v), come get your kid). You’re IT. Kid’s at a play date and she’s delayed, call the other mom to say she’ll be a bit late. You need to establish criteria for interruptions, boundaries. Without discussing them, you are expecting her to use her best judgement (oy). I get your feeling resentful about her not putting in her full effort (household work etc). My husband has VERY old fashioned cheuvanistic views about housework. He comes home and literally DUMPS his stuff (clothing/head to toe, papers/mail) everywhere. Combining his stuff and the messes my kids make and I feel like I’m working backwards with clean-up. He’s got the right to say ” you’re home more, I need you to do more, but there are things I think he should be responsible for. Hanging his suits is one of them. Worse yet, when he complains to me about the condition of the home (I can clean and he says nothing or I clean and my kids undo my efforts with their messes and then that’s all I hear about. It would help to hear what I do right, when I do it, for him to clarify what I’m ok doing (straightening, laundry, dishes, etc) and what I don’t want to do (hang his suits). You guys sound very resentful of each other, but I don’t think that has to spell the end. I think you need to find a way to talk to each other more. Maybe you want to try “I’m going to listen to you all day” day. Give her one day to tell you what she wants and give it to her. Then it’s your turn. You’ll each see what the other wants without each focusing on your own needs.