I have sat in coffee shops not wanting to go into work before, and some mornings with tears streaming down my face, with the stress of covering stuff. With a DH working FT and main breadwinner (but needed me to keep earning as his job was more likely to go in the downturn), a DD with ASD/ADHD, elderly DGPs, narc DM, problematic extended family, micromanaging boss, never ending workload, and being let down by help we had hired in to cover things.
I have learned that it is important to put on your own oxygen mask first, before dealing with others. So make sure you carve out a few minutes for yourself to breathe - and build it to get some exercise (my exercise is fast walking a longer route between the train and office in the mornings).
Learn to ignore things that can be ignored and focus on priorities. So as long as the kitchen and bathrooms are always clean, its ok for other parts of the house to get cluttered while you deal with other stuff. (At least, temporarily).
Make sure there is nutricious food that people will eat. If that means certain conveniences, knowing good local takeaways, doing internet shopping.....do it. If you have a slow cooker or your oven can work on a timer, use those to make it easier. (More on food later).
Clean clothes (I happily spend money on having extra sets of uniform etc, and enough regular clothes to not panic about laundry, and we also wash daily and dry on the clothes horse/tumble dryer, but only fold once a week - clean clothes go into the clean hamper downstairs once dry, then someone (or 2 or even us all) throws them on the sitting or playroom floor on a Saturday/Sunday afternoon with the tv on and folds them, DH always irons on Sunday evenings watching Countryfile while I sort the kitchen end of the room).
Paperwork is a pain - do what you can out of hours, writing notes, recording things said in phonecalls or meetings, or things you've noticed that would be useful for future phonecalls/meetings etc. Send messages by email in advance of meetings to be helpful - it can often shorten the time needed to explain or discuss some points. Set aside a time in your work week that is "lunch" or "personal" - for your phonecalls chasing people who need to be talked to during the day - it might mean that some days your lunch is at 11am, because that's the time you can talk to school teacher....or 3pm because that's the time the Dr takes calls.
Leave each call with an agreed plan of action - "so I will do X and you will do Y, and when you get results Z in 2 weeks you will give me a call" or whatever. Note that in writing for yourself at least (a follow up email to the person, copying yourself, may also be useful). Make a diary note to follow up at the correct point - refer back to the previous specific discussion/email/meeting and the plan agreed then. Because rather than starting each time from scratch, you are referring to an ongoing discussion and agreed plan so makes it much harder for others to quibble.
Whether that's for DD1 or DH, or anything that DD2 potentially needs (or yourself!).
I always find end of the day, when people are tired, and whiney, and hungry, are very hard, especially only walking in from work to deal with everything facing you. So dinner needs to be fast and easy. In our house, I do a lot of prep work after dinner one night for the following evening - it might need to wait awhile while bedtime gets sorted, but when the washing up is being done, I also do things like peel and chop veg and potatoes, take things from the freezer, make a sauce if needed (like a spaghetti bolognaise or curry) so I can just reheat it the following night, marinade meat if needed, …..whatever things I can do to get ahead. I do batch cook, sort of - if I do a spag bol or curry or chilli type sauce - anything that can be frozen - I do at least a double batch as it is a very small amount of extra work (as long as it's not just as I get in from work), and freeze at least 1 other night's dinner - so that only needs to be defrosted, reheated and fresh pasta/rice boiled up - almost no attention needed at the end of a work day. 1 tray roast type meals - eg. chicken joints on a bed of baby potatoes, large chunks of veg and some tomato passata - can get organised in the evening, put into the oven on a timer in the morning and are practically ready to just serve up when you get home at night. Some nights are oven chips and fish fingers with some frozen peas or tinned corn as veg. (That time is also when I tend to get the daily laundry organised too - throw dry things into the clean clothes hampers, chuck what I've washed that day into the dryer/onto the clotheshorse, and grab the next load from the dirty hamper to set up in the washer on the timer to wash while we're out tomorrow - it only takes about 5 minutes at that time compared to 20 minutes when we get in and coats/bags need sorting, homework needs doing, dinner needs to be cooked, post needs to be checked, everyone's daily news and troubles and excitements need to be spilled and supported.... ).
Can DH take some burdens off your shoulders? Does he do bedtime even if his injury means he mightn't be able to bend to do bathtime? Can he do light housekeeping jobs (are there any tools that might make some jobs possible for him)? Could he do homework and reading with DCs?
Can you make some household stuff more "family" and more "fun" than "chores"? It takes a little time at the start to teach the DCs but, say for sweeping the floor, get a smaller sized brush (one from a kitchen playset will still do a reasonable job and is more their size), and give them a brush and pan as well (regular kitchen should be fine) - so both have a tool and a job - and get them to sweep the floor. OK, you may need to do it again later, but it gets the worst done, it keeps them busy, and it teaches them as well.
If you were to do something like a family clothes folding watching a Saturday kids movie, it becomes family time, you are all on the floor together (just make sure the floor is clean 1st), so time to chat and snuggle and watch the movie, you probably do most of the folding but can slowly teach them how to do smaller things, and even just starting by asking them to sort and then ball up matching pairs of socks gets them involved. And then you could ask them to each take their own socks or underwear or pjs to their room to put away (slowly building up from bringing them and showing them where and how to put 1 type of thing a few times, to going with them while you have a different pile but watching and praising, and building up to them doing all their own things).
And getting them to put their dirty clothes in the dirty clothes pile/hamper. A quieter day (not midweek before dinner), show them how you sort whites from darks. Get them to gather all the towels and bring them to the washing machine for a towels wash another day - you might have to get out the clean ones to replace, but they can take a job off you gathering the dirty ones.
If you start to get on top of the house, then you can start to have some more fun like baking together, or teaching them how (on weekends) to cook - whisking eggs, cutting peppers (counterintuitively, use a proper sharp knife and teach them how to use it safely - it needs less effort to cut than a blunt one) rather than onions initially (leave the crying for later!), mixing ingredients together.
and unfortunately, with ASD and injury in the house, family outings have to be carefully planned and ready to change. But by making the house a more relaxed place to be, that should help to grab some time out at home - not always relentlessly cleaning and dealing with being the organiser - and maybe doing some things away from home. Look at shorter outings, making sure there are places to stop and take a break (especially with food or bringing a picnic), or things that you can enjoy part of and go back to do the other part another time (so if you get to a museum, for example, plan to do a specific section 1st, with a different section that you might put 1st the next time).
Sometimes, you might have to settle for part-family outings - DH is not up to walking so you bring the 2 DCs to a park and let them have a good run around.
DD1 is stressed and meltdown-y, so stays at home with DH and you bring DD2 to something which has lots of noise and lights and wouldn't suit DD1.
DD2 is whiney and tired, so stays with DH while you bring DD1 to something which is quiet and peaceful and suited to her needs and interests.
You are in need of a break, so DH takes the 2 DDs to visit DPILs or a softplay that they can both handle or something (or he stays home where they have their own toys and you go out to do something you want to do ).
And sleep. I always feel a lot more overwhelmed when I am in a cycle of not getting enough sleep....
Sorry that's a bit long.....but you sound like you understand the limitations on you and the family, and you are doing it right, you just need some extra tactics and a "you got this" attitude. It's hard, but it does get better over time.