Ethernet has a self-assigned IP address desperation!

The Express that is not working is set to the wrong mode or plugged in incorrectly.

This is going to be hard if you haven't a clue on networks.

1. If I am reading this right.. you have airport express.. plugged by ethernet into main modem router as well as plugged into the MBP..

In other words this particular Express does nothing. Plug the modem straight to the MBP.

Does this work?

2. Fixing networks.. if it is more complicated can be a hassle.. why not employ a computer tech for half a day.. Consider it the washing machine broken down.. and who are you gonna call.. the washing machine repairman.. you don't get out the tools and strip down the washing machine.

3. If you insist on doing it yourself.. (ie you want training for network engineering crammed into a 2min post on a forum) we need exact pictures of everything.. exact layouts and exact setups.

Now, however, it's saying that "Thunderbolt Ethernet has a self-assigned IP address and will not be able to connect to the Internet." In addition, Airport Utility isn't finding the other Airport Express that I have hooked up via Ethernet to my Tivo.

That is not surprising at all. Apple airport utility in later OS is 100% designed for wireless networks..

If you use ethernet did you swap the airport utility over to ethernet.

It is a really obvious place.. click Other WiFi Devices.. an there lo and behold.. the option to use ethernet instead of wireless.. it is such an obvious place to put this option I am surprised you didn't find it. (note heavy sarcasm).

Apple airport utility depends on ipv6 being set correctly.. auto is not correct.

So in the computer make sure IPv6 is set to link-local only.. for wireless or ethernet or both.. any active connection that you hope to get working .. must have this set correctly.. do not trust automatically in any version of Mac OS.. it is wrong most of the time.

Once you can actually bring the airports up on the screen.. click them and post screenshots of the summary page..

ie this one.

You can also click on edit and give us more screenshots from the Network, Wireless and Internet tabs..

Screenshots of the setup as well as showing what is connected to which... helps loads.

Thanks for the excellent screenshots.. that is super.

because the wifi signal keeps dropping (I looked this up - apparently this is an issue with the 2015 MBPs).

Lets start here..

Ring Applecare if you have any or buy some... because Apple should be fixing this .. not you..

Did this issue happen when you upgraded the computer to El Capitan??

If that is the case report it and ask for help.. it is poor apple drivers and poor upgrades that are killing your network.

At least I assume if you had this setup before and working it was ok.

They have both worked, but I had to turn everything off to mess with some cables and when I turned it all back on, this mess presented itself.

Now lets get started..

I want you to try something completely different.

Plug one express into the Sonicnet modem router by ethernet..

Reset it to factory and please change all the names to short no spaces and pure alphanumerics.

The express will be in bridge.. and will create a wireless network..

Lets call it express1 and the wireless AEwifi

Now setup the second express as express2 to extend the wireless. So it will use AEwifi.

Now try and use the laptop by wireless not ethernet.. but if it is an issue plug it into the Express by ethernet.

The way it's configured now is that both Airports are Extend A Local Network.

Just so you know. This is wrong.. it can never work as you have it now.. Extend wireless is purely apple.. apple must connect to apple .. not the wireless of your modem router.

What I am suggesting is you do extend wireless properly by using one express as a WAP and one as a repeater.

I have tried Join A Wireless Network, Create A Wireless Network, and Extend A Wireless Network. Nothing seems to be working.

The first one is correct.. join a wireless network is called by apple client mode.

You must reset the express to factory and redo it when you mess things up.

Here is the way to do it.. direct from the horse's mouth.

AirPort Express: How to join an existing Wi-Fi network in client mode - Apple Support

If it fails.. do not be surprised.. try it the way I recommended .. it is far superior method.

do you know if I could get another Airport Express and add it to the network like I did with Express2 and connect it to the MBP via Ethernet?

Yes,.. you can do that.. it is not the best way to do things but possible.

If the laptop is still within one year of purchase you can buy Applecare.. in the end I think it is worth while to get the support you need. There is no excuse for the wireless behaving this poorly.