"I have a 2010 MB PRO that is telling me the battery needs to be serviced. Would you all recommend that I take the computer to an Apple Store to have that replaced, or is it simple enough to have an independent shop do it for me?"
I don't think Apple Stores will do battery replacements on Macs this old any longer.
That means you'll need to take it to an "independent" shop that works on Macs.
BUT... before you do that...
Replacing the battery on a 2010 is quite an easy task, and you can do it yourself.
All you need are a few tools, a replacement battery, and some simple instructions.
Go to ifixit.com to see what's involved.
BE SURE TO BUY THE RIGHT TOOLS (shouting intentional).
I believe you'll need
- a Phillips #00 driver (for screws on the bottom cover)
- a plastic "spudger" tool (for lifting off the connector, DO NOT USE a metal blade for this!)
- a "star" shaped drive (for removing the battery screws, sorry, I forget the size)
Be aware that buying replacement batteries is "a crapshoot".
They almost never last as long as the original battery.
One other thing...
If you're going to have the back off, you should consider replacing the original platter-based drive with an SSD. They're cheap now and easier to install than the battery!