Yes it is unreasonable.
Rest assured if he takes it to court they will look at all circumstances ~ especially the childrens routines..that will be paramount in their decision as the childrens needs are taken into account over the adults.
Make sure she keeps records of communication. In the event of the kids having shared residency the contact will be split down the middle ~ I can't see it being decided that they are all over the place during the week. Remember this isn't about 'letting' kids stay with their parent..they must be able to decide for themselves where and when they want to go. The adults are supposed to be there to work out arrangements around the children's wishes :o)
With regards to the child benefit, your partner should contact the benefit centre in Newcastle to let them know her change of address and bank account (if she hasn't already). I would recommend she get a totally new account.