Too many opportunities to identify

If I'm correct, when I view a movie on the TV from my laptop, the path comes from the wall plug, to the router (wire), then my laptop (wireless), back to the router (wireless), to the apple tv (wireless) to the samsung (wired).

Not necessarily, the Apple TV has a feature where if you airplay content to the Apple TV that's available from the Apple Store, it will stream it direct rather than taking the longer route.

There are times when there is an incredibly long delay between some action on the keyboard and what shows on the tv, or the signal drops.

I assume this is your main question. The answer is that there could be many things causing this and unfortunately, you may have to try many things. However, first thing first, When you stream the movie and watch it on your Mac, do you get pixelation, stops and starts or any there glitches? If not I suspect the issue is with the LAN and not the WAN (local/wider area network) i.e it's your side of your outside wall. I'm kind of leaning towards this already since you say you have a lapse in moving the mouse when mirroring or extending your desktop to the Apple TV.

Intermittent problems are often a result of interference. Interference can be caused by other wifi networks in the neighbourhood or from many household electrical items.

You can download and install iStumbler to help you see which channels are used by neighbouring networks so that you can avoid them, but iStumbler will not see household items that cause interference.

Refer to your router manual for instructions on changing your wifi channel or adjusting your multicast rate (which may help where interference is present. You might also try moving the Apple TV away from other electrical equipment.

There are other types of problems that can affect networks, but this is by far the most common, hence worth mentioning first. Networks that have inherent issues can be seen to work differently with different versions of the same software or from device to device, so just because it worked before or works with a different device doesn’t exclude interference as a problem.

2.4 GHz networks are significantly more prone to interference than 5 GHz and have fewer channels to try when avoiding nearby networks. 5 GHz is generally faster but is poor over any distance and struggles with obstacles such as walls and floors.

The following article(s) may help you.

Recommended Wi-Fi settings

Sources of Interference

Wifi Diagnostic Software (for Mac users)

You may also find some help on this page, where I’ve collected some of the more unusual solutions to network issues.

I understand that some of the suggested software (whilst once free) has become pay-ware, I suggest you look around, you may find free alternatives.

As for tools, I want information, not raw data. Knowing there takes x milliseconds using Ping tells you nothing unless you know what are good/bad values. When Activity Monitor tells me how many threads something has, I want to find a knitting manual. What's a PID? And how much memory is too much?

A PID is a pelvic inflammatory disease (joking), it's a type of controller I believe that employs feedback to determine the control required. I don't think we need to know about it. You may however need to try to understand the numbers you see. the main one of concern is your throughput, movies can require between 8 and 25 Mbps (HD/4k) anything short of what they require and they will encounter issues. Latency, packet loss, jitter etc etc are all useful in their ways but actually all they do if they are of concern is lower the throughput (Mbps) you can measure your throughput with tools such as Speedtest, but this won't be any use for measuring between devices (only from the internet)