Most Western nations can get visa's on arrival and these are single entry valid for one month. They can only be paid for in hard currency such as dollars, sterling or Euros. The cost id $15 USD or £10 GBP

Extensions can be obtained easily.

Visas obtain from the Egyptian Embassy in advance are single entry and valid for 3 months and are a little bit more expensive in the UK they are £15 GBP

As far as i know it is a visa per passport so the kids should be free. It is quite unusual these days not to have to have a seperate passport for your children so I would just confirm that if I was you.