Old Cat peeing indoors after we got a new cat

[FairFuming]

We have a 12 year old female cat who is normally very good at using her litter tray or going outside. About 4 weeks ago we adopted a male cat who is about 2 years old (he was a stray) they are both neutered. We did introductions slowly and our lady cat has always lived with other cats until recently and it's never been an issue. It's only in the last week that she has started to pee and poop indoors, she has access to litter trays that he doesn't get to but has refused to use them and instead has peed in the only 2 rooms that have carpet in them.
Any idea why she's suddenly doing this? He's getting outside now so is inside a lot less. I keep them separate at night with her having the run of most of the house and him having the kitchen hallway and ute room, I'm now going to swap them around so she's at least not on carpet. Any suggestions for getting rid of the smell? One site in particular just won't stop smelling!

It's bizarre because I'd say for the last week they have mostly gotten on ok, they will come into the same room as each other and just ignore one another.

Sounds like a bit of a protest to me. Hard one to solve.
The only thing I can think of is to use something like Feliway to calm her down a bit, maybe spend more time with her so she feels she has lots of attention/ needs met?
Apart from scrubbing the carpet, not much more you can do. Sometimes multi cat households are very difficult.
Do they both go outdoors?

Protest wee. My cats do it if my neighbour happens to brings her dog round (and even if my cats aren't inside).
It'll settle as they get used to each other but keep her off the carpets at night. Warm water with biological washing powder breaks down the urine. As he's been neutered he wont be spraying.

My cat did this when I had my twins and they became mobile - definitely a protest - several emergency trips to the vets to look for urine infections confirmed that. I put in a cat flap so he could escape the twins and that has seemed to improve the problem

As for the smell - it's a nightmare to get rid of - my cat was doing it on the twins beds and rugs

Lots of dr beckman pet carpet cleaner and order an enzyme based cleaner from Amazon - any old cleaner won't work - you have to use one that breaks down the enzymes in wee. And just keep treating

I also hired a rug doctor and used the specialist pet solution with it

After all that put food down where she is weeing - once she associates it with food and not wee it should improve things

Thanks for the replies. I've gone over the worst bit with an enzyme cleaner for the 4th time then when it dried scrubbed in some fabric softener and that seems to have gotten rid of it finally! We had a Felaway plug in and it's right next to there she's been peeing and the day after I plugged it in she started so I've unplugged it incase it's adding to her stress. We did last night with her in the kitchen and I suspect this will just have to be how we do it for the next while. Thanks for the reassurance and suggestions

It's not a protest - it's stress.

I would personally separate them completely for a few weeks and see if that makes a difference. She's quite old to be getting used to a new cat, bless her.