I want to add a page where users can view and edit a list, problem is the list is not in the site but rather in its parent site. I also want to be able to filter the list so they can only see a items that have a predefined value in a certain column.
I think you should try using Content Query Webpart(CQWP) in your site. You can fetch data from your parent site by using it.
here is a link which might be helpful.
SharePoint out-of-the-box doesn't allow you to display list views from other sites. You have a couple of options though:
1) Use a third-party tool
2) Write a custom web part or application page in Visual Studio that queries the list data from that site and displays it using a GridView or other control on the page.