Hardcode an image in all posts

I know this is a very obscure edge case, but bear with me…

We have a main site that we post press releases to. That site uses WP’s XML-RPC to push the posts to specific legislator’s site(s). We are not using WP Multisite, these are stand alone WP installations. The plugin we use to push the posts does not include the featured image, and to be honest that wouldn’t really work anyway as the photo is in portrait orientation and those don’t look well as featured images since they are a photo of the legislator’s face.

What I want to do is, in the child theme, hard-code a right aligned image to be displayed after the title and as the main body of the post appears. The reason we need to do this is because we want the facial photo to appear when someone shares the post on Facebook, and not the site’s logo. Also, I need to hard code this as editing hundreds of previously published Posts is simply not feasable.

Can someone enlighten me on how to accomplish this? I *know* it’s not the proper way to do this, but I’m in a bind and I need to solve this ASAP. Thank you!

The page I need help with: [log in to see the link]