You need to allow 24 hours after SIM activation for the tranfer form to 'validate'.
If it has been longer than this then
Log out of giffgaff
Clear your browser cache
Delete all cookies
Log into your wife's account and try again
The error 'Something went wrong with your request, please try later' is often caused by an issue with the PAC you're entering. This could be any of the following:
If you're certain you've entered the details correctly, please try using a different browser or device. If the issue persists contact your old provider and ask them to re-confirm the PAC. When they reply that it's correct, ask again!