Is natural to omit the definite article before mom/mother and dad/father meaning one's mom or dad. For example:
Mom says that I don't have to clean my room.
I will ask dad if I can take his car.
By dad and mom I mean my mom and dad.
Articles – Correct Usage of Definite Articles Before ‘Dad,’ ‘Father,’ ‘Mom,’ and ‘Mother’
articlesdefinite-article
Best Answer
In your examples, no - you would not use the definite article "the".
You are using "Mom" and "Dad" as proper nouns, and in written form they should be capitalised. Most people do not call their parents by their forenames, so "Mom and Dad" are substituting for these.
In most situations where you are referring to your mother and father, you would say "my mom" or "my dad" to make it clear you are referring to your own parents. When you refer to them this way, there is no need to capitalise them.
We only use the definite article "the" when it is clear which specific thing/person/group you are referring to, and as there are many, many moms and dads in the world, "the" wouldn't necessarily point to yours.
An example where you might use the definite article with "mom and dad" is if you had established a context in which there is only one set of parents, for example: