An encrypted disk image is useful to prevent anyone getting access to it unless you authorize it (by entering the password). Once you've authorized access to it, it's just another volume (disk) that's visible to the Mac and its users, just like any other file on your boot volume.
If you talk about other users, I assume you mean giving them access through network file sharing?
Now, you might have noticed that if someone connects to your Mac using file sharing, he has to enter your Mac's user name and password, right? Unless you allow Guest access, in which case anyone can connect as Guest. But Guests can only access certain shared (public) folders.
Now, you might also have noticed that you can create new users on your Mac, using the System Preferences, Users & Groups. If you create a new local user, he gets his own private folder area under /Users/. And now, if someone logs into your Mac, he can use either that new user name or yours. Eitehr will only give him access to that specific user's folders.
With that knowledge, you can now create a special user that only certain people may have access to. Tell them that user's name and password. Copy the to-be-protected files into that user's Documents folder. You can then also use Finder's "Get Info" on those files/folders to choose who has access to them, i.e. that the owner (that specific new user) can read, but not write. That way, no one can mess with the files, they're read-only. Make sure you apply these ownerships to all enclosed folders, using the gear icon in the Get Info window. Then test this and make sure that a remotely logged-in user can indeed only read but not modify those files.
Hope that helps.
Add the disk image to System Preferences→Users & Groups→Login Items.
Put the password in your keychain.
Accept that you've just thrown away part of the value of encrypting the disk image.
There is some remaining value. An intruder can't open the disk image with only your disk or the disk image or a copy thereof to work with. But they can open it if they can get control of your computer while you're logged in.
At the least, disable automatic login, and enable "requires password to wake from sleep or screen saver".
Best Answer
Ok, finally I managed to solve it by myself. Probably there is a faster way to do this, but I didn't find it out, so I went the most obvious way:
Create a new encrypted disk image with Disk Utility, making sure of leaving the "Remember password in keychain" checkbox UNCHECKED (it seems to be checked by default), then I just copied everything from the old encrypted disk image to this new one and finally, I just deleted the old one.
That annoying dialog is not bothering me anymore.
I hope this is useful for someone else.