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There is an old saying in the theater: "Anyone who puts kids or animals on the stage deserves what happens to them." That means that no matter how well-behaved, or well-trained you think they are, at some time they are going to revert to their true nature, and you can only hope it doesn't happen during a performance. The SL correlation is: "Anyone who uses groups deserves what happens to them." That means that no matter how well-behaved or how well-trained you hope they are, groups don't play nicely with anything, and especially not states, clicking on, and triggers. Sooner or later, you are likely to have problems with them.

I used a group in SL once, and it worked the way I wanted. I think it was in 19... No, wait. I'm thinking of another program, Maybe ... Well, it doesn't matter; the point is that groups don't work in SL. Pretty much you can use groups, or you can have triggers and states that work, but not both. No amount of extra work is too much to avoid the problems that come with groups.

Of course, by now, I know your experience leads you to agree with me, so I'm just preaching to the choir in hopes it can help steer somebody else away from the siren allure of groups.

As to your problem, no amount of extra work is too much to avoid the problems that come with groups. Fortunately, there are a lot of ways to do what you want without groups.

1. Maybe the simplest, now that you have created everything, is to right click the group, and export it as a picture. Then delete it, and insert the exported picture, which will work with clicks and states.

2. My preferred method is to create everything as one object.  Start with a rectangle, fill with a background, then right click to add text to it. It's still one object, and only lacks the picture, which can be added as per #3 below.

3. A somewhat more complex method is to add the shape, then create the next element, like the image. Copy the image, edit the states of the shape, and in the Normal shape, paste the image. End editing, and repeat for all the elements of the former group. It ends up looking the same, but is considered only one group.

4. Create the entire group in a graphic program (which will give you a lot more flexibility and options), save it, and import it into SL

All of these methods allow you to have one single object with all the elements you want, and none of the problems associated with groups. You can create and modify their states any way you want.