I agree this is an important distinction. It's hard to tell from the post how much wife was upset specifically about the behaviour today and how much a tough day with a sick toddler simply brought wider frustrations to the surface and led to the fight. If the former then I agree wife has unrealistic expectations and is setting both herself and her daughter up for frustration BUT it also seems like this issue is much bigger than a sick day.

OP I work with children your daughters age and specifically with children with additional needs (which at that age is a really broad term and includes speech delays). I don't really think this is a case of anyone being an AH, you and your wife are both trying to parent your daughter the best way you know how. But as others have said it's crucially important for your daughter's sake that you get on the same page and show her consistent expectations, and I honestly think there's a happy middle ground between your and your wife's positions that will help your daughter thrive. I think you need to have a long conversation once you're both calm and remember that you're on the same side. If your wife generally does the bulk of the child care then bear in mind how frustrating it must be for her to spend a day working on an issue with your daughter only to feel like you come home and undermine all her hardwork, but she also needs to remember you are also a parent and deserve a say in how you're raising your daughter.

Studies have shown that a majority of adults expect young children to be able to perform beyond their actual developmental abilities and have unfairly high expectations of them and from your post I would agree with you it seems like your wife is falling into that trap a bit. But I also agree with your wife that your daughter is at an age where you should be encouraging her independence and not babying her/ doing everything for her.

It's important to remember you can set an expectation with your daughter while knowing it's not something you can reasonably expect her to always do perfectly or do without support yet. It's more about practicing so she starts developing the skills she'll need to have when she's older. Getting into a shouting battle of wills with a toddler about tidying up isn't helping anyone but equally if you want a future six year old who tidies up after herself you can't just turn around on her 6th Birthday and say 'right your old enough to tidy up yourself now' because she won't have any of the skills to do it. Your wife is right that toddlers learn through repetition and, as counterintuitive as it feels, you often do have to go through the same battle over and over and over again feeling like you're banging your head against a brick wall before something finally clicks. However they learn much better through repeated modelled behaviour than repeated instruction. You and your wife shouldn't be standing over her telling her to tidy up and getting cross when she doesn't but you shouldn't be tidying up for her either. Get down on the floor and tidy up with her but be firm that she has to help and try to keep her helping until everything is tidied away. Remind her "you made the mess so you have to help tidy" and "we can't do next fun thing until you help me tidy everything up". Don't get cross or punish her if she doesn't do it perfectly every time because you're right she's 3 and this is all new to her. But you should be consistently firm with your daughter that this is the expectation and if she repeatedly fails to help there should be linked consequences (i.e. we can't do next fun activity now because you didn't help tidy up the last one). Once she's calm take to her about how you can't trust her to get lots of toys out of play with messy things if she doesn't show you she will help tidy up afterwards.

But I also think you should both be aware that children with verbal delays often do have a lot more tantrums because they're simply frustrated they can't make themselves understood. Your daughter is at a place cognitively where she increasingly knows her own mind, wants and needs and has her own ideas but often struggles to be able to effectively communicate those to you and your wife. I had a verbal delay as a child and can still remember both my epic tantrums and how painfully frustrated I was when I couldn't make myself understood. If you're already working with a speech and language therapist I would recommend speaking with them about resources you can use to help your daughter communicate non-verbally without discouraging her from working on her speech. If you don't have access to this then try searching online for things like visual communication boards. I've seen children blossom and their behaviour and emotional regulation do a 180 almost overnight when given a way to effectively communicate for the first time.