It sounds to me like she is training four young orcas how to hunt - I doubt she is training them how to be a family, unless family is defined as 'orcas that hunt together'. 'Family-in-training' means they are learning to do something. The something could be anything, so you'll have to look at the context to be sure of what it is.

IN-TRAINING means someone (or animals in this case), is in the process of learning to become something. In this case the group is apparently not quite a family yet, i.e. still learning, which doesn't quite make sense. It's confusing to me what they mean by that.

It means that they are not blood-relatives but they have decided to live together as if they were a family. So they are practising being a family.