'British Isles' has no meaning in law.
If your granddaughter's birth was jointly registered by your daughter and her (ex-) partner (or if the ex has obtained parental responsibility through a court order), it's an offence under the Child Abduction Act 1984 for your daughter to take your granddaughter out of the
United Kingdom, without her father's permission, for more than one month at a time.
The Channel Islands are
Crown dependencies of the United Kingdom but they are
not part of the UK. (That's why they're not in the EU). So, assuming that your daughter's ex has 'parental responsibility' (through co-registering the birth or through a court order), he's correct in stating that his permission is needed for your daughter to take your granddaughter to Guernsey.
http://www.ips.gov.uk/passport/apply-child-rul es-parental-responsibility-rules.asp
Chris