Many prisons, in addition to normal visits arrange “family day visits”. These are held periodically throughout the year and are arranged by either the chaplaincy or the family unit within the prison. Commonly these visits are open to all prisoners who have small (ish) children, grandchildren, nephews and nieces etc.
The prison system is acutely aware of the stress a period in custody places on a relationship and they do try to make these events into relaxed and enjoyable events with games for the children, face painting etc arranged. Some prisons also relax the restrictions on visitors bringing in food to share during the visits which can last up to 3 hours. These events are advertised on the notice boards within the prison and places can be limited.
Some prisons actively help children who visit understand a little more about what the parent in prison is doing, with pictures of what a typical cell looks like etc. These services are provided by volunteers who help out in the Visitors Centre’s; check on your specific prison page to see if this is available.