I am an Australian living in Chingola about one hour away from Mufulira, I have children aged 4, 6 and 7. I am married to a Zambian and doing mission work here.
It won't be easy but it is manageable as long as you can live without some luxuries that you may be used to.
I hope you will have a decent preferably 4wd vehicle as that will make life a lot easier for you. Not sure what supermarkets are in Mufulira but I assume there will be at least a Shoprite. Being an hour from Kitwe you will find most things you need there if you can't get them in Mufulira.
You will need to make sure you have a house with a tank and a pump for water (even better if it has its own borehole), as water supply can be very erratic, and perhaps best to get a back up generator unless you are living in town centre and can cope with the occasional power cut.
There is a trust school in Mufulira which is probably reasonable but there are some good schools in Kitwe and Amano Christian School in Chingola.
Feel free to contact me if you have any questions.