Yup you need boundaries, and they need boundaries. The current situation isn't working for you or them.
- Don't go into their room.
- Don't do laundry... especially if it means you invading their privacy.
- Strict rules for communal areas of house - if they don't like it they can move.
- You cannot insist on their private space being up to your standards. Unless it's going to invite critters in, let them live in their own squalor!
Make a clear division between private and public space. You may well find they are a lot more respectful of house rules if they are treated like grownups, and that means you respecting their right to privacy in their own room.
At the moment it feels like you've both made a deal with the devil that means everyone feels badly done to and entitled to more than they're getting. Never ends well.
They pay a pittance in return for leaving their adulthood at the door. Suspect they are taking the situation and you for granted as they feel it's a trade off because they have no privacy and right to decide how they live.
You feel they have to live exactly to your rules, and because they're paying a pittance, they don't have a right to privacy or to make their own decisions.
Tbh I would be furious about you invading my personal space and rifling through all my stuff for my used underwear to wash! Gross invasion of privacy, ugh! That's because I'm not a child and I have a right to my own space, and with that I have a right to do my own laundry and tidying in that space :) I think you're thinking martyred thoughts about 'having' to do their laundry because you expect, and don't get, them living in exactly the way you want to run your household. But switch that around. Think about being free to do your own clothes, in your own way, when you want to, as a 'right', not a chore you're taking off them as they won't do it 'properly'.
However this right to privacy and freedom to make their own decisions about how they live only extends as far as their own room! Then, it's all about your rights in the rest of the house (within reason of course!). They certainly don't have any rights to make the rest of your house messy or dump their stuff around it.
Ultimately it's all up to you, as it's your house. However as they are not children anymore and they pay (nominal) rent, they would be reasonable to need privacy & to be treated like grown up housemates/ lodgers vs naughty kids.
I'd be making rules very clear. And making it clear that once rules and rent has been agreed, if they don't abide by them they have the choice to move out.
And that's fine.
No flouncing or emotional blackmail needed, as they are grown ups living on extremely good terms in another grown ups house. If the terms are not acceptable to them, that's fine, because they have the option to go. If the terms are acceptable and agreed, then everyone sticks to the rules, just as they'd have to as lodgers in someone else's house.
They don't have the choice to treat you like a skivvy or treat your house like it's their own (in terms of communal area standards). Or rather, they can do that, but they can't expect to do that without consequences. And that consequence will be to be asked to move out. And you need to be ready to abide by that, and not let it descend into a situation where everyone blurred boundaries and disrespects each other (which is what the current situation seems to have descended into!).
Their bedroom, their rules... within your household, your rules!
They get their own room, in exchange for rent & abiding by the rent agreement. You're giving them privacy and the 'right' to deal with their own laundry, tidying, cleaning etc. In exchange, they get to abide by your rules and standards throughout the rest of the house.
Cooking / kitchen use is likely to be another flash point, so you'll have to have clear rules and expectations for this.
Are they expected to eat with you sometimes for example? Or do they cook & eat separately as a lodger would?
What foods are 'communal' and up for grabs? And what isn't? Maybe you could make staples communal and give them a bit of cupboard space for extras/ special stuff that they buy for themselves? Likewise you have foods just for you and your dh, which are not for pillaging.
What happens in terms of food running out? Do you have a system for shopping lists and what goes on your weekly shop? I can imagine grubbing around the kitchen discovering what they've used up would be infuriating and keep them in the 'irresponsible teenager' type of role!
I'd also make sure they're paying enough rent so you're not paying for loads of their food on top. Show them the amount of their rent that gets used on food. And what gets used on household cleaning products etc. And how much you are subsidising them, with electricity / internet, water etc (possibly compare to figures for one bed flats in the area?), so they understand how much they are getting as part of the deal/ or free. If they've fallen into the 'kids' role in the house, they may well be taking all the 'hidden costs' for granted, and jerking them out of that attitude will help get things on a better footing.
Are you happy to cook dinners for them for them to eat when they get back? Does this mean they're locked into coming back at a certain time? I'd personally limit this to x times a week, or certain days, or confirmed x amount of time in advance.
Anyway, good luck with getting the living arrangements to be on a more grown up level, where mutual respect and clear rules and boundaries mean no one feels badly done to again.