I have ND kids who have always struggled with screentime. I think the best thing is to observe patterns and change based on what you're seeing - so if it's causing such a stress to come off, then it's not really a good wind down activity, or possibly it's a symptom of something going on at a different point in the day. I read this great book called Self-Reg by Stuart Shanker (the EU title is much more wordy but it's the same author) and he points out that a child sitting quietly does not necessarily mean that they are calm, and it's easy to make this mistake and think ah, they are quiet, so they are calm, they are winding down - but they can actually be just as overstimulated by all the input from the screen, the movement and colours and sounds.
You said that this has got worse since re-instigating morning TV - so it might be that she can cope with morning TV or bedtime TV, but not both. It might be worth experimenting although of course don't chop and change too often as this will be confusing. But it might not be that you have to go cold turkey. That is definitely an option and it can be a chance to sort of "reset" and then cautiously add things in and observe.
A lot of the time MN advice can be very rigid or theoretical and I don't think it's actually helpful in practice - watch out for "If my kids did this then I'd do that", because it's probably not based in experience, sometimes posters even have a kind of superiority complex thinking because they have always had limits on screen time, that's why their DC have never struggled to transition away from it (or there has been minor protest at worst). Whereas in reality it might be the other way around - their DC were naturally more easygoing around TV, so the limits worked well. All children are different.
It is helpful to read posts which are in the past tense ie things people have actually observed/experienced/tried with their own DC.
I also think the narrative about screen time on the internet today is not helpful. It's not actually going to melt her brain. Yes, algorithms are designed to be addictive, and a lot of the content on youtube in particular can be especially absorbing in a probably-not-very-healthy way. But I do think if it's specific programmes she watches, especially if they are normal TV e.g. BBC, Nickelodeon, Disney, Peppa Pig etc - this is not the same thing and it's more like the TV that was accessible to LOs 20+ years ago, before youtube etc.
Accepting her feelings and holding a boundary is good. If I would nitpick slightly, it says in the book How To Talk to beware of using "but" because it basically invalidates all of the great feeling validation you were doing. To see an adult-relatable example, try this:
"I know you're tired and busy with the kids all day, but this place is a tip!"
vs
"I know you're tired and busy with the kids all day. This place is a tip!"
The first sounds like a dismissal, like the main point of the discussion is to berate the partner for the house being a tip and the speaker thinks being tired and busy is an excuse. You can imagine the next sentence being all about what "you" should do to fix it.
The second acknowledges the struggle, may perhaps be a bit jokingly accepting, and you can much more easily imagine following the speaking partner offering some suggestion of help or support or problem solving.
With young children it can actually help to totally separate the two points, e.g. avoid mentioning the complaint in the sentence at all - only start with "I know, it's so hard to stop watching TV!" and let her process/go through that before you try to shift gears into "Now it's time to go upstairs for bed". BTW if you like the How To Talk books, there is an excellent app accompanying them (Android Link) which I have found helpful for remembering what to do in the moment.
Your Parenting Mojo had an absolutely brilliant series of podcasts recently where she interviewed TheGamerEducator. I think only the first one will be useful with a 3yo - but strongly recommend these. Really good, nuanced take and I learnt some new things.
Sorry this is becoming a barrage of recommendations and don't think I'm suggesting you consume all of them at once(!) but I do tend to squirrel away resources and this is a good one - there is a book on Kindle for 99p called When Your Kids Push Your Buttons, and I ADORE this book. It was so good for me and helped me a lot with boundary setting and exploring my own worries/guilt/etc. It sounds to me like you are under a lot of pressure, and you're worried about the effect on your DD so you are focusing on things like - OK she needs TV to help her unwind/downtime, she needs me to always be lovely and nice and accepting and never critical. You aren't doing anything wrong by working and having her in childcare. Does her dad carry this guilt? Clearly not based on what you've said, so why is it your burden? You say the childcare setting is homely and she is happy there, and you do lots together at the weekend. I think this is great and you're also working hard to provide her a nice life and security. So please, give yourself a break! 
If you are worried about any overstimulation at childcare, perhaps speak with the provider about a midday "quiet time" - my 6yo has recently started doing this at kindergarten (not school, we are abroad) and it has DRAMATICALLY helped his moods and self-regulation during the rest of the day. I honestly am amazed because I didn't think that he needed it, he hasn't napped since he was 2, but it's really helping him.