The noun inflexibility refers to a lack of adaptability or inability to bend. Inflexibility is not a good trait for a gymnast.
The noun inflexibility can refer to a metaphorical inability to adapt or change shape. It is the quality of being rigid or not capable of being bent. Your inflexibility when setting rules for your kids is hampering your relationship with them because the older ones don't want to have the same curfews and bedtimes as the younger ones. Unless you want a mutiny on your hands, consider revising the rules to age-appropriate limits.