Basically, one approach you can use is to open your website via InAppBrowser plugin (loading your site in separate window instance ) which will retain simple browser functionalities like opening a links in a new tab. Thus, you can always go back to your hybrid app content by closing this window and use some native features.
If this is something similar to what you aim to achieve, you can test it by verifying whether you have enabled the InAppBrowser plugin from Properties > Plugins window in our client.
Then open your website using the plugin:
For additional information regarding the InAppBrowser API please refer to its online documentation.
I hope it helps.