For example:

When Ray killed the cat, I ran to tell his Stacey.

This sentence doesn’t make sense using the real name “Stacey”, so no capitalization is required:

When Ray killed the cat, I ran to tell his mom.

Consider another example:

“Boy, is Randall going to be mad when he finds out I used his new driver to kill the cat.”, sighed Ray.

This sentence does make sense using the name “Randall” so, capitalization is required:

“Boy, is Dad going to be mad when he finds out I used his new driver to kill the cat,”, sighed Ray.

Does this help?

RE:
should mom and dad be capitalized?

My mom is pretty. Mom is pretty. I was talking to Dad. I was talking to my dad. Get it? It is capitalized if it is used as their name.

“I told Mom that I loved her cooking.”

In that sentence it’s her proper name.

“Typically, moms and dads are a child’s best friend.”

In that sentence it’s just generically referring to all moms and dads and should not be capitalized.

“I told Dad I’d do the dishes”

“I love you, Mom!”

“I don’t want to do homework, and Dad told me I didn’t have to”

If not, then don’t capitalize unless it’s the beginning of a sentence.

“I told my dad that I’d do the dishes”

“I love my mom” etc etc