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From the scenario you described, I have a clue what may be the problem here.
Are you able to view the field(s) which link from the epic to the initiatives? It may be possible that there are different fields used in your instance. The default field should be the field "Parent Link". There it should only be possible to select one parent issue. That's why it is strange that you get two parents for one child issue...
But there is also the field "linked issues", where you can choose between different links between issues, like "relates to", "child of", "parent of". Maybe this field is also used in your instance.
For the right display of the Parent-Child hierarchy, you should check the configuration of Big Picture. You can configure the field, which you want to use for the hierarchy in Big Picture via Tasks -> Task structure, as shown in this community question: https://community.atlassian.com/t5/Jira-Software-questions/BigPicture-How-to-Set-Display-Order-by-Hierarchy/qaq-p/1375815
My guess is, that there are more than two fields configured and used in your instance. If you don't have access to this configuration, you can ask your admin to check it.
As I mentioned above, I am not a 100 percent sure, if this is the solution for your problem, but it may be a first direction for troubleshooting :) Maybe someone from the community can add some more hints and insights ;)