The correct sentence is:
This is my mom and dad.
The reasoning behind that is you are saying "This is my mom and this is my dad", not "These people are both my mom and dad."
The second sentence is syntactically correct, but is semantically wrong. It is weird to say that your work is "swimming, running, shooting and jumping every day" (since those are actions rather than "work"), but you should rather say:
My work is hard. It consists of swimming, running, shooting and jumping every day.
A less harsh alternative that you can use in verbal communication is:
My work is hard. I have to swim, run, shoot and jump every day.