You "covered" your first roundline meter (where you added the mouse action) with the second meter... so you cannot reach the first meter to have the mouse action work.
You can add mouse actions on the second meter, and they work...
So you can "see" the first meter, but the second meter is covering it, so you cannot click on it... You have both meters the same size and starting at 0,0?
You need to change the order of the meters in the ini or create separate skins and send a !Bang to change the ZPos (which skin is on top) in order to have mouse actions work on the topmost skin.
Right now the mouse only reaches the last loaded meter.
To change the zpos, you need to create a meter that executes a !Bang to change the ZPos of the skin configuration.
I am not that familiar with using the !ZPos bang, but here is some info on it from the manual:
!ZPos [POS] (Config)
Changes the z-position of the window. -2 = OnDesktop, -1 = OnBottom, 0 = Normal, 1 = OnTop, 2 = Topmost.
Check the manual:
http://rainmeter.net/cms/Bangs
I not sure I understand what you mean by "another meter can trigger the mouse action too" ...
I would get in the habit of using LeftMouseUpAction= for mouse clicks, that way you can use MouseDown to move the skin position on the screen.
Also, you do not need the !Execute anymore, just ["C:\"] works with the latest rainmeter.