To have decided not to host this friend at my house until I've gone to hers

Cos that's how the dynamic works with my friends.

Maybe she feels she can't live up to your standard of hosting. Having a cleaner round and preparing a meal for a visit from a friend is a lot. I've never lived by the taking it in turns to visit either and nor do any of my friends or family, there are people that prefer to host and people who prefer to get out of the house.
Leaving her child's pooh in the bathroom and walking in with muddy shoes is taking the p though. I'd be more concerned about this than not having an invite to her home. It could be easily solved by making arrangements to meet elsewhere.

If she is such s good friend, of such longstanding, just tell her the rules of the house are “no shoes” snd clean up after yourself.

I have friends who I very rarely go to their house, easily er fur me to have them at mine or out so doesn't bother me. But this isn't the issue here. The issue is her just imposing herself at her own convenience. Learn to say no. Also stand up and say 'lovely to see you but I'm bushed' and escort her to the door.

If she turns up just say you're going out or whatever and don't let her in or to stay more than a short time.
Also, there's no need to provide food for everyone unless you want to.

you hate people in your home

but you turn up unannounced at theirs? Why?

I had a newish friend who did this. I don’t see her much any more.

The problem (as on so many MN threads) seems to be that you don't like this woman. Why on earth are you pretending to be friends with her? Friendship is when two people enjoy each other's company and admire each other's personalities. Not forcing themselves to endure the company of someone they find annoying.

If you actually like someone all these transactional "rules" stop mattering. Some people enjoy hosting, some people don't like it, everyone's homes are different sizes, it's as simple as that.

I think it's probably best not to invite her again. Not because she needs to invite you to hers, but because inviting her to yours is putting you out so much.
PPs have suggested good strategies if you did want to have her over, like telling her what end time you have for the visit. You do need to be forceful enough to enforce this though, which depending on the friend might be ruder than you are comfortable with. A blanket ban is sometimes easier.

I think she has different standards to you, doesn't invite you over as maybe her house is a bit scruffy, and she enjoys your clean tidy place. Maybe her family are used to this and don't care, but she feels she'd have to make an effort to clean up for you. Like you, I like to prepare for guests. TBH, she sounds a bit of a nightmare, personally I'd keep meetings to park, café etc. If you enjoy her company, have her over but be really firm about shoes off at the door and maybe make up an appointment you have late on, so they/she have to leave by a certain time.

People who turn up unannounced here don’t get invited in.

Anyway lots of harsh comments here saying why let her turn up late etc etc they're not harsh comments, they're just expressions of how others enforce boundaries.

If you are happy with someone coming any time, then you say that and accept the fact they might come at any time. If you have a window say 2-4, then you say 'yes, you could come at 2 but I need to be finished by 4'. Then if they arrive at 3, you still show them the door at 4.

Boundaries have to be articulated and then stuck to. Then if someone keeps pushing, you put them in the 'not a friend' category and say no next time.

I have an open house. Anyone can drop in any time for any reason. As a result, everyone knows that they are welcome but the house won't be a showroom. They are also told the rules - my house is your house, go anywhere, use anything and lounge on a sofa as much as you want, muck in with dishes and cleaning, bring snacks. I have one set of friends with the same attitude and I stay with them 100 times more than they stay with me as they are rarely in my neck of the woods. Life is easy when you are not keeping score and when friends visiting is not a major event.

I agree OP that it's incredibly rude for her to continually expect you to host her and never return the favour. Anyone with an ounce of politeness and manners wouldn't do this.

Stand your ground, OP. And I'd actually say to her 'Not until I've had an invite to yours!'

I can't see anything about her behaviour that deserves the title of friend, CF acquaintance seems more accurate. Do you get anything positive out of this relationship?

If you don't want to host her then don't. It doesn't sound like you like her much anyway!

Hate people in my house and often turn up unannounced to friends' houses. If they are busy or out, that's fine and I can leave. Not a problem here.

One of my pet hates is people just turning up unannounced. I think it's really rude. Time to put your foot down and tell her to message you first to see if it's convenient. If she just turns up say it's not a good time and don't let her in. She will soon stop just turning up.

This 100%

and kinda invited herself over, turned up a few hours late so I couldn't run errands in the morning and I know I didn't have to make so much effort but felt obliged to use my day off to ensure cleaner came, tidied whole house, cooked food for all of us and planned something fun for them to do. She didn't stick to shoes off policy when we nipped back to use bathroom despite having returned from a muddy park and her kid left literal sht on my toilet seat.She was the last one to use bathroom so she didn't clean it either*

I dont understand WHY you would allow ANY of this to happen?

You're allowing her to walk all over you and then whinging about it afterwards

Why do you do this?

My DH has been funny about this with playdates. I would always assume that if someone doesn't invite you back that they have a good reason. My DD's best friend lives in a tiny flat, and her mum has never invited us to hers. DH thinks this is super weird, but I come from a culture where if you want to build a relationship, you host. People have all sorts of reasons they might not feel comfortable doing that.

That said, if you actually don't like hosting her, just stop inviting her. If she is rude and doesn't follow your house rules, she doesn't sound like much of a friend.