Changing childrens surnames in scotland after a marriage?

my partners ex is getting married in a few months, she has threatened to change their childrens surname to her new husbands. My partner was never married to her but his name is on their birth certificates and we have the children ever weekend for visitation and financially support them. we live in scotland, can she legally change the childrens surname without my partners consent? It worries me because he would be devistated and it is only being done out of spite over an arguement about a custody issue! what are our rights to keep the childrens surname?