The handwashing struggle reminds me of autism or adhd and sensory overload- doesn't mean he's on the spectrum, but you might do some research and keep your eyes open for for other signs. If hes on the spectrum diagnosis is easier as a child, and there may be resources for both you and him

I have ADHD and was a pretty sensitive child myself, and struggled with the sensory feeling of hand washing for long time

For the hands, are his hands dry? They might be irritated and washing is unpleasant because of that?

Ask for help on things like the dishwasher, give them a bit of power to help their situation, they might help, they might make it harder on you while "helping" but the offer and possible help might make it feel like they have agency.

The mom thing I have no advice, it comes and goes in waves. My kid varies who's #1 between me and Mom, but really, it's always Grandma, or the dog.

What does he say about how he is feeling?

What does daycare say about his behaviour?

Father of three here. Sounds like a mixture of giving in to all his demands and him demanding your time and attention. So keep at it not giving in to all his whims just because he melts down.

That being said, the things you describe sound more like genuine sadness and dispar. Leaving you kid all day in daycare, they might have a genuine and relatable need for your time and attention. I understand that's the economic reality for many people, but children need their parents time and attention and at that point he has not only waited all day to see you, but is also probably tired and has no more patience left.

Putting him to sleep is about comfort for him that he knows. For a father there is a time to start doing that so he gets used to it. Have you tried bringing him to bed when your partner is home? Start together, but you read the bedtime story or whatever. Then gradually reduce your partners presence until you can go it alone. Be aware that he might actually insist you bring him to bed on days your partner is home now.

Finally with things he needs to do but doesn't want to: give him a few minutes to get himself to do it but make sure he knows there is no way around it and when his time runs out you do it anyways. Usually they prefer doing it themselves instead of being forced to do it.

Being that sensitive at that age might be a sign of more things like autism or ADHD, but much more likely its a sign of how he is used to getting what he needs which might often be attention not what the fight actually started. Try encouraging him to spell out what he needs from you and doing things independently from you.

E.g. "go wash your hands while I unload the dishes, if you are done when I'm done, we can play immediately"

Finally: TV is not the devil and if it gives you an hour to calm down yourself and have the energy to deal with him properly, that is fine. Just don't use it to calm him down or avoid confrontation.

Sounds like you have a full day and a full life. You can do it! :)