Why Iraq? Would it be better/more up to date if he used Afghan?
He knew 2 years in advance he was going to Iraq
Possible, as long as he is not talking about a ground war. Regiments know where they are on the Ops Cycle 2/3 years in advance. The very last troops in Iraq came out in 2009, so make sure he gets his dates right.
He flew to Bagdad then straight on to Death Valley
No, British Military don't fly into Bhagdad.
He received instructions from his General
Unikely - What rank is the soldier? The CO (Lt Col) is more likely to give his Regiment 'the plan', The OC (Maj) will instruct his Company in detail.
Some other soldiers arrived at the house to collect him, dressed in sand coloured uniforms
Context required - are these mates that are going on Ops with him? Families do quite often take their soldier to camp to wave them off, others prefer to say their goodbyes at home.
Also, the dad reappears at the end as a surprise seems unlikely to me
Surprise to who? If the kids, then yes, I know wives that do this, but very unlikely a wife wouldn't know the date of return (unless he's been injured / been flown back early for a specific reason).
Lastly, do all families with a dad in the forces live on a base?
No, but if you are talking about a Regt where they all move together then more will than wont (housing is much cheaper). Or do you mean 'inside the wire'? Most quarters are on a patch away from the actual Regimental Buildings IYSWIM. Families don't have to go through a security gate to get home.
Hope this helps, happy to answer any more questions 