Oh OP, it feels like you're getting a rough ride on here, and you have my sympathy. The world is divided into different camps of people, and I'm with you, I struggle to ask for help or what I need or want. For others, who are much more comfortable in asking for help, we can be seen as martyrs, or expecting people to be mindreaders, when that isn't the case, we just operate differently.
I'm definitely learning that I need to vocalise the things I want and need rather than wait for things to be offered or suggested but it's not easy. In your case, through necessity, I think you might need to be brave and look at different things you can ask of people so you're helped, and your DH too, and you can mentally switch off from the continual problem solving.
For your mum, she's local and more than able, can you delegate some specific stuff - can she collect DC from school, run them to any activities and maybe sort out dinners a few times a week? Could you she take your DC to her house for an evening or overnight? Could you ask her over for a coffee and while she's there, could she do a couple of loads of washing? Or, could she take some with her? You can even say that you don't like to ask for help, but you're finding this really hard and you wondered if she could help for the next few weeks with a set pattern, so you're both clear on what you need and what she can sort for you. She may be delighted to help, or she may not - and if it's the latter, then that stinks but you know where you stand.
As for friends, could you ask if they can help with DC with school runs, kids activities or playdates once or twice a week for the next few weeks - there is an end date, it's not a massive ask, and people will be happy to help.
Foodwise, could you do an online order for something like COOK? The food is tasty and nutritious, and your older DC or DH can just put them in the oven without having to do much prep. Takeaway twice a week to lighten the load?
You're frustrated, in pain and feeling hurt - all of those things will add up to one big emotional mess, and I'm not surprised you're upset. Everyone has their own stuff going on, and I would imagine most people would love to lend a hand if they know you need it. Don't see it as asking for help, see it as giving your friends and family a chance to support you.
Then, once things are easier, look at ways to support yourself while you heal. Focus on great TV programmes and films, read brilliant books, listen to podcasts, tackle the stuff you've been meaning to for months/years or catch up with admin or look up your family tree. It's crap that you've broken your leg so badly, but also try and see this is an enforced rest from the usual To Dos, and see what can you do with the time that will make you feel good.
Sending lots of love and healing.