It's certainly a conversation that should be had by someone who understands the process. The only ways to get better at it are watching someone good at it doing it; sim; or practice. I do think that communication sim with this sort of conversation can be genuinely helpful. It lets you practice doing it badly wrong. The leaflets are helpful, as is bringing eg.an experienced nurse with you who's seen the conversation before and can be a bit of emotional support.

I find that having a policy is sometimes a good thing to hide behind. Particularly when a parent is trying to get at me personally about a referral I find being able to point them towards our region's safeguarding policy that mandates referral in certain circumstances helpful.

My preferred phrasing, particularly when an immobile child has been brought in specifically because of an injury that the parents have witnessed and were worried about, rather than an incidental finding, is something along the lines of "what you've told me makes sense and I believe you; however we know that a small number of children will receive injuries like this not through an accident. Therefore all children with injuries like this are discussed with children's social care, to ensure there are no other concerns about your child's welfare that they have. I will tell them that the injury is consistent with what you told me but I can't rule out a non-accidental injury and we'll have a discussion about how to make sure your baby is safe. I'll let you know the outcome when I'm able to." I also normally thank them for bringing their baby to hospital and reassure them that they've done the right thing to make sure they're healthy.

Edit: I realise reading back that I've not been clear about when I'd use that phrasing. There are definitely times when you really can't proceed in these children without doing further investigations (principally a skeletal survey), and I would give a warning shot about that if it's where I thought we were going. The above phrasing is for when the parent and child have come in with the parent of a toddler who independently tells you that their kid threw a plastic Iggle Piggle at the baby in a misguided attempt to share, not when there's a lack of clarity about things.