Sunshine and sleep work wonders with that awful, constantly tearful anxiety.
Don't ask the kids if they want to go outside, they will say no because they are happy doing what they are doing. You need to find a way of just getting the three of you out there for at least an hour a day.
Have you got any big boxes? Chuck all the little bits of dolls and stuff in those and take them outside, with a rug or blanket.
Get them to make a fairy tree or a village or a school or whatever play they like doing with the dolls.
Take out simple drinks and snacks - fruit, cheese, yoghurt, raisins, crisps - whatever comes in a packet without any stress.
If you can, get them to eat breakfast/lunch/dinner outside. Just set it up, get them to 'lay the table' on a rug. Picnic style. They get to choose the plates etc.
Just sit with them. Don't worry about 'doing' anything. Just be outside. Get some air. Get the sun on your face.
A bowl of water and a flannel can waste hours with plastic tat toys. Get them washing everything and anything. Again, outside. They are getting benefit without any stress.
Get them to set up their own mini obstacle courses so they can race each other or race the dolls. They don't need to actually go fast, just get their legs moving.
Crayons and paper and tracing tree bark or peoples or patio or anything. Just to buy another 10 mins in the garden.
Book a time each day that your husband can keep an eye on them whilst you take a walk. It can just be for 20 mins whilst he has lunch. Just go. The first time will feel impossible. After a few days it will be part of the routine and it won't be so hard. Stick some music or a podcast or something in your ears if you need an incentive.
The lack of sleep is horrific and makes everything worse. Being out of the house means less mess to clear up (chuck it all back in big boxes and don't think about it again) and a more genuine physical tiredness.
If you wake up, try and find a way of calming down. Go to the loo, get a drink, listen to the calm app if that works for you (makes me more awake but seems to work for others!), write a list of all your worries so you can forget about them whilst you sleep.
It doesn't matter if other people can cope. It really doesn't.
See if your dh can take a couple of long weekends with leave rather than a week or so. He might be more open to that and it spreads things out for you. Nothing worse than him taking leave and using that as an excuse to do even less!
When he wants to do the garden at the weekend then the kids need to be out there with him. He can get them to help or set them a task. Carve yourself an hour to do your own thing and then crack on with the essential jobs.
Foodwise, keep it simple. Make one/refrigerate or freeze one. So double quantities, half the decisions.
It all feels overwhelming but one little thing at a time. You can do it.