Oh I am so pleased to read about someone else's child who wakes a lot and screams loudly. Not just mine then.
It is so so knackering and frustrating, it can't help but cloud your life.
The sleep - likely that this is at the root of much of your sadness. Bloody hard to stay positive when you are permanently busy and exhausted.
Do you & dh share the sleep deprivation? Can you get turns at having unbroken nights?
The weight issue - you are doing everything right, now you just need to drop the guilt. You have nothing to feel guilty about, you are a parent doing her utmost to care for her children. What more can you possibly do?
The teeth - He doesn't need a filling, great. Did they mention anything about the enamel? Sometimes children's first set of teeth is low on enamel (apparently? I was told mine was one) and they can decay v. easily.
Schooling & socialising - could you ask the school for some advice? Or work on it a little by organising playdates with a couple of children he likes? Or a regular activity with one of his friends?
It seems to me that once they feel happy and settled (friendships), the learning takes off.
You & dh - do be kind to each other, young children are very demanding and put the strongest relationships to the test. Remind yourselves and each other that these days of sleep deprivation will pass and that when you are both getting more rest, it is likely you will feel a lot less stressed.
Heavens, you are doing so much! You sound like a lovely, caring mum and I think you deserve to feel pride for all your amazing achievements - working and raising children is huge.