Hi! I am following up on my original post from 9/6, asking about my trees. I am including new photos. As you can see, the older tree is starting perk up a little, with some leaves coming out even in higher elevations. The other tree however, is not doing so well, with nothing growing other than the suckers at the bottom. Does anyone have any thoughts as to what I should do next? My wife thinks that I should give up on the second tree and cut it down. However, the other tree she thinks should be trimmed. I did cut off a few small lower branches. They were quite dry. Thoughts?

Can you get some close-ups of the leaves and stems? Especially the one in the middle of the yard?
The one up against the house could be a problem in the future as it's really close to the house and could cause issues with the foundation.

Here is the first thread, for context it probably would have been better to continue there but the link will at least fill in the history.
The thread "Brachychiton populneus- will they survive?" in Ask a Question forum

I thought they looked familiar.

Here are some close-ups.

I agree with your wife that you should remove the one up against the house and trim the other. It would be best to start at the top and remove dead branches first. Once you have that done you can decide whether to remove more for shaping, leave it alone, or remove the whole tree. If you can water out toward the tips of the branches it will speed up the regrowing process.