Alternatives are:
1. If you can use a keypress to hit the Accept button, then do that, and put it in your mapped key. Sometimes dialogues in Windows respond to SPACE or ENTER to accept the default button. If the dialogue does not have a default then this wont work. EQ1 I believe allows you to set a hotkey for Accepting group invites, so may have a similar ability for other dialogues. Lotro has a default on
some dialogues.
2. You can setup a multiple step (or round robin if you prefer) mouse click (I use SHIFT+MOUSE1 for this, but you could use any key), and then set a
Sync Cursor Action on the first step. This way you can move the mouse, and then spam SHIFT+Mouse1 to send a Mouse 1 action to all windows, and it will cycle through them all (I break this down and have multiple steps instead of using round-robin, so I can put a popup for when I get to the end). You
still have to move the mouse to get the location, but this setup is also really handy for dealing with those pesky NPC dialogues that wont let you have more than 4 toons access it at the same time.
3. Turn on broadcasting and click all at the same time, although with F/ship invites in Lotro this means you will probably get a random order group.
Of course as in most games, you should have the UI layout exactly the same. If you move a dialogue around then you are pretty much hosed with either Sync Cursor Actions or Broadcasting.