HSBC have well thought out personal Internet banking. The ability to create payments without needing some sort of approval step at the bank (as Nationwide do) is particularly welcome, as is same day transfers to other HSBC accounts. They are introducing telephone confirmation of certain payment instructions as a defence against phishing and identity fraud. Make sure that you keep the phone numbers the bank has up to date!
HSBC is a very secure site, they seem to have a good sense of security, essential for reliable online banking.
In particular they have introduced additional security measures for business customers. A key fob system. I have not much experience of this, but a small business I do work for sometimes uses this.
I cannot rate child specific safety as I haven't seen anything relating to children as yet, but have no reason to feel it is any less secure.
I wish you all safe banking