DON'T GO BACK!
Seriously, they sound dreadful. They have had ample opportunity to rectify the situation.
Take some more photo's as evidence and go somewhere reputable to have the extensions properly removed.
Get your daughter to write a letter to the salon documenting what has happened and requesting a full refund plus an additional amount to compensate her for all the damage they have caused. Put a total amount in words so that this is unambiguous.
In the letter give them seven days to reply and tell them that she will take further action in the County Court if they do not comply.
Also, when she has them removed, ask the new Salon for confirmation of the damage caused.
Finally, issue a summons in the County Court, if necessary. Your local Citizens Advice can help with this.