Petting a bird anywhere apart from the head is intensely sexual for them. Birds who are friends will preen each other's heads. Birds who are mates will preen all over the body. Stroking under a bird's wings, their chest, and especially down their back or around the vent is basically the psittacine equivalent of making out or even having sex.
Having a bird who thinks you are its mate is unfair on your family. Your bird will see them as rivals for your affections, and will be more likely to be aggressive towards them in an attempt to drive them away. It is also incredibly unfair on the bird. Mated pairs are around each other 24/7. They preen each other, they forage together, they sleep next to each other, they fly almost touching wingtips. You simply cannot offer that level of companionship and understanding to a bird, because you are not a bird.
As such, you must limit yourself to headscratches only with a parrot. Even then, not all parrots enjoy being touched. There are a number on AA who have lived with their human flock for years without wanting to be pet. If you want a pet who you can reliably stroke, give headscratches to or cuddle, don't get a parrot.