I feel for you, s-man, that would be off-putting. My son wais his mom when he is apologizing for something, although he has a way of exaggerating it to the point where it is pretty clear sometimes he is taking the piss, which is kind of funny to see in a 3-year-old. Otherwise, its hugs for Daddy. Go ahead get hugged. The child needs to be able to function in both cultural environments.
My son and I shake hands when he makes a promise, and by the way, I think all farang fathers of sons have a responsibility to teach their boys how to shake hands properly. It is something Asians often get horribly wrong.