It's weird to think we live in a world where the only way to keep in touch with one's relatives is video chat.
LW, if you want to stay in their lives but have minimal contact with their parents, at that age my suggestions is: write them postcards. Fun postcards. Lots of postcards. They will see the pictures and know they are from you, and the parents can read the short notes to the kids in a way the parents are okay with until they are old enough to read themselves (You don't even have to write anything - I have treasured postcards from cousins when I was that age that just say To Melannen Love Cousin.)
You will be always remembered as the fun cousin who writes postcards, and you will make sure they have an ongoing line of contact with you if they want it. As the kids get older, if they want to stay in touch, you can move onto letters, and then arranging methods of contact that don't need parental intervention, but when they are toddlers: postcards are great.
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LW, if you want to stay in their lives but have minimal contact with their parents, at that age my suggestions is: write them postcards. Fun postcards. Lots of postcards. They will see the pictures and know they are from you, and the parents can read the short notes to the kids in a way the parents are okay with until they are old enough to read themselves (You don't even have to write anything - I have treasured postcards from cousins when I was that age that just say To Melannen Love Cousin.)
You will be always remembered as the fun cousin who writes postcards, and you will make sure they have an ongoing line of contact with you if they want it. As the kids get older, if they want to stay in touch, you can move onto letters, and then arranging methods of contact that don't need parental intervention, but when they are toddlers: postcards are great.