I don't believe that parenting is or should be different just because your location is different. The still problems and requirements exist - for me, they just come about in a different language. Our problem is that being an American parent, I absolutely insist that my daughter speak English very well with my husband and with me and always with us, Georgian is allowed with everyone else. That is because before she was two years old and whilst she was playing with Georgian speaking playmates, she began to no longer speak as much English with us at home, so, I put my foot down about the language factor. In the States, we have Georgian friends whose children understand Georgian when spoken to, but, will not speak it themselves. I do not want the same to happen with my daughter regarding English, whilst we reside in Georgia.
I believe being an expat parent has positively influenced our parenting and our family life because I am able to be a stay-at-home mother whilst my husband works. Were we in the States, both of us would have to work and someone else would have looked after our daughter much more than us, essentially raising her. I think she has truly benefited from having daily parent care.
Try to enjoy the richness and diverseness of culture as much as possible, whilst retaining your own and instilling and maintaining an interest in your own country to your children. Where you come from and how you were formed is essential to who you are and therefore, who you are as a parent and central figure to your children.