Hello,
Sorry for the troubles you are having.
I would think two Event/Calendar Plugins would not work on the same site. There is to many similarities between the plugins to there is going to be conflicts such as what you are having. That does not mean it is not possible for them to work.
It could be the slugs are the same for both plugins.
In the Events Calendar you can change the main view slug and single event slug here:
Events > Settings > General Tab
Then these are the two fields I would look to change.
Events URL slug
Single event URL slug
Change those to something else and then test again and see if that works.
There maybe other issues that come up as well, we can try to help out, but for the most part 3rd party plugin compatibility is beyond the support we can provide.
Let me know if changing that helps out.
Thanks