I say - delegate! Can DH help out with the thank you cards? or gift buying for MW?
I agree with other comments- don't feel pressured about time frames.
The letters to GP, politicians, etc are not urgent - no rush needed there.
And don't feel bad about unanswered emails- people understand that you are busy with a newborn (and 2 other children).
This is such a precious time- try not to spend it worrying about what you SHOULD be doing (I know it is easier said than done).
xx