I send an email with 2-3 photos that look great. However, when someone replies to that email and chooses to include the original photos with the reply, my photos return to me looking distorted and ugly. Is there a way to prevent that?

Also, when you mention "email service providers," does that refer to email clients such as Spark or MailSpring or Outlook? Or are you referring to the ISPs like Comcast, ATT, etc.? Or more like yahoo, google, apple mail products that can either be client based or web based?

Yes, all of them. Apple's iCloud Mail service does not alter image resolution. That means both sender and receiver need to use @iCloud.com email addresses (or @me.com — they are synonymous). So if you want your images to be sent in full resolution use iCloud or some other service that you are certain will not alter their resolution. I don't have any particular recommendations.

As for the others, I don't know. I happen to know AOL was one of the first who did that and it caused a stir. Today it's pretty much accepted.

Web based or Mail client based makes no difference. Regardless of the client you are using, it's the email service providers that mess with email messages — and if you were not already aware of the fact, the implication of that is that they read them, for a variety of reasons. Of course it's not a human being who's reading your emails, but there is no guarantee of that either. Don't expect privacy with email.

Mail stinks at a whole lot of things including some of its common uses, and acting as a stinky file transfer service (here) being among those stinks.

All sorts of folks involved in the mail message transfer can shrink or compress attached images, particularly among the free providers.

What to do? Send the recipients a link: Share photos and videos with an iCloud Link on iCloud.com - Apple Support

I have also tried the "Actual Size," "Large," and "Medium" settings with the mail app but that does not seem to have an effect either.

After you choose a resolution for the attachment, Apple's Mail client does not alter it. It is sent to your email service provider exactly as you choose to send it.

However, a variety of email service providers are notorious for changing image resolution, on either the sending or receiving end.