Writers are frequently confused about when to capitalise words such as mum and dad. It isn’t as complicated as it may seem. The general principles are as follows:
I'm cooking dinner for Mom She asked Dad to mow the lawn "Oh no," said Grandma
This applies if you are using the word as a title as part of their name:
We went to visit Uncle Gareth "I've got things to do," said Grandpa Joe
If you are using the word as a label – a description of relationship or kinship – you should not capitalise:
I'm cooking dinner for my mom Jenny's grandmother plays tennis He looks just like his brother
You can usually tell if you need a capital letter by substituting a proper name and deciding if it sounds strange:
I told Mother the cat ran away I told Helen the cat ran away
I told my Mother the cat ran away I told my Helen the cat ran away I told my mother the cat ran away
This isn’t foolproof because people do say ‘my Helen’ or ‘our Helen’ to distinguish between multiple Helens or to imply relation. However, the use of a possessive pronoun (my, your, his, her, our or their) is often a good indicator that you should not capitalise.
This is my second post on capitalisation (the first one was on capitalising months and seasons), and it is an expanded answer to Erik Porter’s question about whether to capitalise mom in the phrase my mom. I hope it helps!