We love children so much. Preparation can assist, to some extent. As when I think about it, it is the home where the child resides which has stair gate/s and other safety equipment. We need to be observant, and encourage little ones to stay close to the Responsible Adult they are with for the day. As children are naturally curious, and can be adventurous.
Our society has a culture of admiring children and their healthy natural development. We need to instil Health and Safety as an ISSUE from a young age in an attempt to protect from accident, injury etc. We can only do our best, but if we explain to children that the fire is "burny" hot, "Don't touch" just like I recall my elders doing with children. We hope to keep them safe.
Children in our family have still had slips, falls etc just like many others. Us adults and children learn from these experiences. We luckily have had only minor injuries, which healed well. First Aid knowledge and skills can be beneficial, and maybe should be encouraged for all Carers (parents, GrandParents, Aunts, Uncles, etc,etc). As with children we may need to respond to their trauma, and would want to respond appropriately.
Yes it is natural to feel concerned when someone we love is hurt. Elizabeth 1, yes I agree MIL ( Mother In Law) may well have been in need of a hug. She is part of the family, and loves the Granchildren. Accidents can happen, no matter how much we try to prevent them. It is beneficial to know how to deal with them :- First Aid. Also maybe to remember that the family love and invest lots in children, and want the Best for them. Team Spirit.