His guys I bought a shimano Alivio FC-M410 Crankset 170mm along with a compatible bottom bracket about a year ago. The derailleur I had, shimano SIS did not have sufficient range and was old so my LBS (Sportchek) told me I needed a new derailleur and they installed a new shimano SIS for me.

The problem I'm facing is that since they put it on the range has not been enough to push it into third gear properly. They said that any derailleur will not have any more range than this.

Its actually quite strange. What happens, is that I need to push on the shifter harder when shifting to the third cog after having already changed the gear and even then sometimes the chain gets to the the third cog but it is on an angle and just goes back to the second cog. I have to wait for a couple of tries before it catches on and sometimes it feels like its forever before the gear will change.

When you say range, I gather you mean in-out travel. FDs don't vary all that much in trael range, though some are more generous than others.

Usually FD range problems aren't the FD, but the position of the crankset too far from the frame's centerline. Standard chainlines (measured from the center of frame to center between the inner and outer rings) are someplace between 45 and 50mm. FDs are designed around those standards, so if the chainset is too far beyond 50mm they won't reach.

Take a look at the chainring/chainstay clearance and if you have 5mm or so to spare, talk to the dealer about moving the crank in. The method for doing this varies according to the crankset and bottom bracket.

BTW- if you only need a hair (1mm+) you can sometimes get it easily with a file. Find the exact place blocking more outward motion and see if there's material that can be removed. (this varies by FD, so it's up to you to check).

If you put the derailleur on the small chainring can you push it with your hand over the big ring? If so it just need to be adjusted. Sometimes they can be hard.

I'd call that the lateral stroke .. if you back out both limit screws how far does it move?

between hitting the seat tube on the inner direction .. and max outward motion ..

Did you put the new mtn bike cranks replace road cranks? If they , did you can fix the problem by using a shorter bottom bracket. Road cranks are designed with a 45 mm chainline and mnt cranks with a 50 mm chainline. A road derailleur will not work with a 50 mm chainline. Just measure your chainline and you should know.