I have zero time but suddenly have money. What can I buy that saves time

Not sure things are the answer here! A cleaner would be. Mine just has a key but we’ve had the same cleaner for years and trust her. I know you’ve said it’s not an option but seriously look at whether it could be accommodated.
Is it enough money to reduce hours at work?
I used to outsource ironing but don’t anymore as just stopped ironing completely.

Online grocery shopping delivered - get an annual pass - you can do it while waiting at kids activities.

If you're cash rich cash could you take some unpaid parental leave?

If you mean appliances and the like @Inheritednamechanged a robovac for both up and downstairs, dishwasher, tumble dryer and air fryer for quick meals without effort.

You do sound stressed so if you can, ensure that you have a few hours to recharge, somehow. 🌸

You need help rather than things.

A cleaner - I'm sure there is a way to work it around you jobs!

Some childcare - let someone else sit outside kids activities while you have a few hours to yourself.

Someone to help your elderly parents so there is less for you to do.

Don't understand why you can't get a cleaner? I loved having mine, would have one again in a heartbeat if I could afford it.

Laundry service.

Meal kit delivery service - can be 'proper' food but you don't have to think about shopping or deciding what to make.

My absolute honest advice is find a cleaner you trust, get a key safe so they can let themselves in and out and outsource the stress.

I don't sell my son's clothes. I buy a Vinted bundle of basics/nursery clothes and some stuff I like too. I donate the whole lot, I'd say his clothes and shoes cost me a max of £100 a year.

You can get cleaners to keep your keys, or is the issue shift sleeping? If shift sleeping is an issue, you could get a fortnightly clean, and you can even get a hotel to sleep (I spend 40-50 quid on a hotel to refresh every so often!).

Lastly, care for your parents - can you outsource that, again, even fortnightly? A cleaner for them, a meal service, someone to take in their groceries etc?

Have you got a robot Hoover? You could just give the kids clothes to charity shops as maybe buy their new ones from charity shops to save admin.

Pre-chopped veg, especially onions.
Robotic vacuum cleaner which can also mop.

Good quality ready meals can be just like meals you’d cook yourself, not processed - eg we buy them from a local farm shop. I’ve also heard good things about Cook if you have an outlet nearby.

When we were very time poor we used a service that collected our dirty washing then returned it washed, dried and folded. Luckily had an enclosed porch for pickups and drop offs.

Keep a running list of all small DIY jobs (assembling a new shelf, putting up pictures, etc) and when you have a few on there get a handyman in.

Pay for occasional deep cleans at times that suit you around your job if you can’t get a regular cleaner.

I'm not clear why you cannot get a cleaner "because of your working patterns" as a cleaner would be my first port of call.

I am ok money wise, but physically unable to complete a lot of household tasks.

I have a cleaner and someone who washes and irons my clothes for me. I'd also pay for a gardener if I needed to.