I am a British national working in an EU member state. We will soon be applying for the EU permit for my non-EU wife and step-daughter. Do I have to stay in the UK with my family for the first six months or can I work outside of the UK?
This answer assumes that you are planning to move to the UK, or at least your wife and step daughter are planning to do that, and you want to know if you can work elsewhere for six months after they've moved to the UK.
Such a plan is questionable at best under the principle of derivative freedom of movement for non-EU family members of EU citizens. The point of that principle is that preventing non-EU family from joining EU citizens who exercise their freedom of movement constitutes a restriction on the EU citizen's freedom of movement. Therefore, derivative freedom of movement applies only to family members who accompany or join the EU citizen.
Therefore your wife and step daughter do not qualify for derivative freedom of movement in any EU country unless you are also in that country. Obviously, if you move to the UK with your wife and step daughter, they would not be required to leave the country every time you took a short trip elsewhere, but remaining outside the UK for six months for a non-UK job is likely to be seen in a different light.
Your best bet would be to establish your domicile in the UK, somehow, and maintain temporary accommodations elsewhere in connection with your temporary employment there. But if I were you I would not try to undertake anything like that without first talking to a competent lawyer.