Which of these sentences is correct: Can either one be used and still be correct grammar?

Since you have a plural pronoun ("our") you need a plural noun ("hearts") . Some people think it looks weird, as if there's an implication you EACH have multiple hearts, but in fact, this is correct. The following sentence is also correct:

Employees must park their cars in the assigned spaces.

It looks like each employee has more than one car, but in fact, multiple employees, multiple cars.

Go with number 2.

Though for number 1 you could say,"You will always be in our collective heart."

You said our which is plural, so you have to make hearts plural. Unless all of you are sharing the same heart. Then you have full permission to say it. :]