The therapy animals were caught on camera as owner Kevin McVey tried to get them back.
The animals will no longer appear at public events after footage showed them being dragged along the ground at a Christmas fair.
Brother Arthur is "completely upset" after his twin was taken in a break-in overnight.
Movements have been restricted since bluetongue virus was discovered at a farm near Bangor in November.
Several animals were killed after a fire broke out at Animal Farm Adventure Park in November.
A committee is told it is "utterly bizarre" that gulls are protected while the "cute goats" are not.
The two newborns have come on leaps and bounds since being abandoned in freezing cold temperatures.
Rescuers are left shocked after two baby goats are found dumped in a bin, hours after being born.
Goat brothers Boomer, Dingle, Tootle and Tumble help recycle Christmas trees by eating them.
