OP, what seems like a mammoth task now, will seem so much easier in a few weeks.
I’ve four and I think the jump from 1 to 2 was much bigger than the jump from 2 to 3 or 3 to 4. And probably more so when you’ve had help. I’m not knocking you for that - parents and in laws all offered to have our kids/do pick ups etc and like you, I was, and still am very grateful. I think there can be stigma on here around those who do have help and it can be a race to the bottom from those who don’t. Which I never understand as everyone’s circumstances are different.
Anyway, to help you with practical advice:
Do practise this week. I see your parents often got DC1 ready even prior to DC2. Therefore work out what works well for you. For us, it’s the, getting dressed upstairs before breakfast, breakfast, hair and teeth downstairs. No tv at all in the mornings as that becomes a flash point.
If it takes you ten mins to get to the school, plan on giving yourself 20 mins. It’s not really a trick of the mind, but it really does help. You don’t get so sweaty trying to get out of the house with all the random things that kids throw at you as you are trying to get out of the door; toilet run, socks hurting, lunch box isn’t the right colour etc etc.
As DH will be out at work, if you can, in a few weeks, try and get yourself up just 15 mins early. Have a shower and a drink and that wee. You will feel so much better for that time to yourself and with no one in the house later on except you and DC2 you can nap in the morning in the morning once the school run is done.
My kids were all breastfed. First two exclusively. Then DC3 came along and like you the morning feed was taking an age. For my MH, for the sake of the oldest (making sure they weren’t late into school as that made them anxious, not that the school ever said anything), for the baby so they didn't pick up on my tension, we swapped that morning feed to formula and bit later on to expressed. DH was sometimes able to give that feed. And if not, it was quicker anyway.
Get a star chart or something for DC1 so they cooperate a little easier.. Let the school know too that there have been a few teething issues. They can and will have gentle chats.
This is only temporary. You will be fine soon. It will come naturally. At post partum plus 10 you are still leaking every where and a hormonal mess! At least I always was.
In the meantime, phone your mum and ask her round for a coffee. No agenda, just because. And I’d suggest you take it on yourself just to arrange the wrap around and tell her when it is done. DC1 already enjoys herself with her friends so chances are she will like it. And it saves your mum stressing about it.
xxx