You are NOT A CRAP MUM!
Stop thinking that, right now!!
P1 sounds over tired and overexcited . She was probably vastly excited about the idea of P3 & now he's here he just isn't measuring up to her idea of what a baby would be like & she's disappointed. He's not like a doll/teddy bear & for her, he's pretty boring & taking up far too much of your time.
Couple of ideas - can you pick her up without P3 & maybe have time for a ten minute treat for 'Mummy's special big girl'??
If not, can a friend of yours pick her up? She almost certainly won't act up with a friend - most children reserve their horror times for Mum 
And you must try (& I know it's easier said than done) to stop being anxious about P1 & P2. They'll pick up on it, you know they will.
It's very early days indeed - 4/5 days post birth in many cultures you'd still be in bed & not doing school pick ups etc.
I know it's all so easy for me to say & so much harder for you but things will work out and right now you are the most important person in the family. You must get as much rest (I can hear you humphing!) as you can & try not to worry too much about P1 & 2 - they'll be fine.
Always around when you want to grumble or cheer or scream.
Sending you much love & (((xxx)))