Hi,
You need bypass capacitors and place a 10uF capacitor across the power pins of the Tx at the radio pins on the PCB.
Why do you need D1, D2 and D3?
Have you measured the voltage on pin8 of the Attiny to see what your supply voltage is?
You may need to program in a delay between power up and when you send your data.
When designing a PCB remember, you have bought a completely clad PCB and you are paying someone to remove the cladding, so try and leave as much on your board as possible, cos you own it.
All your PCB tracks can be a lot wider for a start.
Tom.. 