For example, one add-on changes URLs (Long URL Plase), the other shows additional information for them (WoT), but for unchanged URL.
How to make "Long URL Please" run before "WoT"?
Unfortunately I don't think this is a problem that could be solved by anyone but the developers of the addons themselves. Try to contact / send feedback to the developers of both addons, and say what your problem is. Hopefully it would be a quick fix they might be willing to look into.