When it is their name, Mom and Dad would be capitalised:
Dear Mom and Dad,
I am just writing to let you know, that although everyone has a mom and a >dad, you are my special mom and dad. So, Mom,
I just want to say ‘brava!’; and Dad, ‘bravo!’. I’ve just been telling
Sis, that Mom’s new coat is so cool. XX
Here's the commentary from an exercise from BBC English on Line
...to have a roast chicken lunch with my mother. I can't wait! - mother
does not need a capital 'M' as it is not being used to replace her
name. If I said, "I am going to lunch with Mum", it would need a
capital letter, but "I am going to lunch with my mum" does not.