If screenshots are OK, and you are just looking for a quicker method than using three or four apps, you might want to consider the Workflow app. It's an automation app with a fairly simple (for automation) interface.
I've made a quick flow that lets you pick an image from the Photo Library, opens and image editor pre-set to the crop tool, resizes the image, then opens the email dialog with the image preloaded.
Basically, once you've taken the screenshot, you just use the workflow and send the email. If you've got standard text and or email addresses for the email, those can be added with a somewhat more complicated workflow.
Here is how the flow looks.
This is the email interface after the flow has done all the previous work. There is an image editor for cropping before this. As you can see, I just used a screen shot of the workflow app as the example.
The workflow can be saved as an icon to the home screen, for easy access, or as an extention in the sharesheet for more universal access inside of apps: or both.