Per my understanding, you might want to open a popup window in host web page though your app part.
As the app locates in a different domain, the popups inside the app will only display relative to the page in the app part, not the host web page.
A workaround is that, you can use the HTML5 PostMessage API to send communication between app part and host page in SharePoint to make the host page react to the request
from the app part.
About how to work with PostMessage API in SharePoint, a demo below would be helpful: