Children hide food when they don't feel secure. Kids in foster care often do this - and as you say, it's not even food they like. Kids in foster care will hide rolls in their pockets and put them in weird hideyholes in their rooms, or as you say, cans of food they don't even really like. It's like a security defense mechanism.
"Eating: Odd eating behaviors are common, especially in children with severe neglect and attachment problems. They will hoard food, hide food in their rooms, or eat as if there will be no more meals even if they have had years of consistent available foods. They may have failure to thrive, rumination (throwing up food), swallowing problems and, later in life, odd eating behaviors that are often misdiagnosed as anorexia nervosa."
The above is from a website that talks about attachment disorder. This could come from the child feeling like the mom doesn't care about her, thus the sending of her to the dad so much. Or it could come from the dad not seeming to care about her, but it usually stems from the person the child wants to care about her most, not seeming to care about what happens to her.
Could she simply be hungry do they feed her enough, have they asked her why...it doesn't mean she has been abused .I sit possible she doesn't like her Dads food and brings her own ..?