Translation:זה האוכל של הכלב שלי.
So grammatically is it "This food belongs to the dog that belongs to me"?
I think technically it says "This food of the dog of me" since the word "belong" is actually שייך.
Correct, but sounds like an archaic textbook. :-)
what about זה האוכל לכלב שלי
זה אוכל שייך הכלב שלי
should be right, right?
No because that's it's food belongs , that's not an exact translation.