Hello Jenna,
Yes you are. Don't know if you have noticed but you are tagging onto a thread that is nearly 5 years old. It's always better to start a new thread as answers can get out of date. The mouse you have didn't exist then.
It appears you have a Magic Mouse 2 that is recharged via a charging cable. That being so a mere two or three minutes will give you enough charge for an average days work. The two hour plug in you mention should give you more than a months usage. It doesn't just die without warning unless it is damaged. You should get a notification when the power level gets to 10% or so.
If you are not getting this much power and it is dying without notification and it is less than 12 months old get it back to an Apple store for the genius bar to check it out.