That's a good idea to have someone look at it. Make sure that it is a store that has worked with hammered dulcimers before, though. Lots of "folk" music stores have no clue how they are strung or tuned. I was surprised. A lot of stores "assume" that if the first note is a C#, for instance, that it just goes up the scale from there. Not so. And with nearly 2 ton of pressure on the sound board from all those strings, if you incorrectly tune several of them, or don't have the correct gauge wire on it, you can blow up the top. Seriously!!!! LOL. You might be better off to find a luthier that builds them to assist you. If you pm me your address, I might be able to direct you to someone in your area.
If you bought it as a kit, though, I would guess that they gave you the correct gauge wires.
It's VERY tricky to string up a new instrument. If the bridges aren't exactly right, it won't tune correctly across the bridge. As you already know, hitting the string on the left side of the bridge gives you a different tone than the exact same string on the right side of the bridge. Your dulcimer is probably supposed to be "5th" tuned, which means the notes are a fifth apart across the bridge. For instance, it looks like that is a 13/12 or 12/12 size, so your bottom note should be a C# on the right side of the treble (center) bridge. The next note up on the right side of that bridge should be a "D" (to start your D scale) and the same string on the left side of that bridge will be an "A".
Every 4th string starts a new course, and usually they are marked by a different color of delrod (the plastic rod that you have sitting on top of your bridge to hold the strings up). Those markings give you a visual clue as to where your notes are on the dulcimer. On that size, you should have markers at "D", "G", "C" on the treble bridge (which tells you which key you are in, too). So your delrod would be (for instance) black for the C#, white for the D, then continue up with 2 blacks, 1 white, 2 blacks, 1 white, etc. to the top of the dulcimer. The bass side is the same, except it would start with a white because it starts on a scale root (G). Did your plans come with a tuning chart?
If you want to try aligning the bridges better, temporarily mark on your bridges (sticky notes) your main courses on the right side of the treble bridge (D, G, C) and the corresponding notes for the left side of the bridge (A, D, G). Then put just those strings on and nudge the bridge left or right (and it will be angled, too), until those 6 markers play the correct notes. Then fill in with the remaining strings. Make sure you are using a good chromatic tuner! <grin>
Sounds WAY more confusing than it really is. The hammered dulcimer, I think, is one of the easiest instruments in the world to play because of the way the scales and keys are laid out.
You'll LOVE it when you get it tuned just perfectly. There isn't a more fun instrument in the world to play. It plays "church music" so majestically and sweet, but you can also pound the crap out of it and get rowdy bluegrass or old-timey string music! Depends on your mood! LOL.
PM me if you need a tuning chart or anything. Sorry for the length of this post! I get excited about dulcimers...can you tell????