I lived in Nigeria for 21 years, my mum was the expat. My sister has just moved back with her primary aged children. It can be a wonderful experience as long as you are prepared and careful. Choose where you will live carefully, gated communities have better security and Abuja is said to be safer than Lagos, although even Lagos is getting better. Private schooling is expensive but worth it. I had a fantastic childhood which I wouldn't change for anything. Corruption is not as rife as some suggest ,perhaps just a bit more obvious than it is in the West and there is an increasing desire among the younger generation to improve the country and its image abroad.
I've only been to Abuja for a week on business, but I had a friend who lived there as an expat for a couple of years with small children and she enjoyed it. Abuja itself was much easier than I thought it would be - it was well organised and clean with good facilities. It is a very new, purpose-built capital city. Lagos was a whole different world away - our hotel was filthy, I didn't feel particularly safe, but on the plus side there was probably more entertainment/night life there.
Hopefully, someone will come along who knows the place better, but don't give up on it yet.
My husband has been offered a job in Abuja in Nigeria. We have 3 children all primary school age. Are we mad to consider this African adventure. Would love to hear from anyone who has done the expat thing out there