dealing with hollow teers

I'm hoping to get suggestions about how to deal with two trees on our property.
1. The first is a large tuliptree (Liriodendron) which has a circumference of about 80 inches. I suspect that it was struck by lightning at some point, as it has a large scar running down one side of the trunk. When we first moved into the house, I cut down a dead dogwood next to this tuliptree that had a shattered crown and charred streak running down the center. Perhaps lighning jumped from the tuliptree to the dogwood? Anyway, there is a mouse-hole sized hole at the base of the trunk, and I can insert a bamboo stake about 15 inches back into the trunk. Wiggling the stake around suggests that the hollow is quite wide.
The tree appears quite vigorous; it blooms in the spring and seems to have a healthy crown of branches. But if it collapses, it could hit the house, or in the other direction, it could completely cross our street. I have an arborist coming to look at it later in the week, but I thought I'd ask here first. Is this a good candidate for removal? I hate to remove such a large, beautiful tree (and I shudder to think what it would cost), but I don't want it to drop on my living room.
2. The second is a sweetgum (Liquidambar), about the same size as the tuliptree. It's a beautiful big tree that shades our house in summer. It used to have a smaller secondary trunk (~8 inches diameter) that a previous owner cut, presumably because it was leaning over the house. The smaller trunk was cut on an angle to shed rain, but even so, it is starting to rot out. Is there anything I can do to prevent the rot spreading to the main trunk, or is that inevitable?
Thanks. Nick
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Find an impartial, consulting arborist at www.asca-consultants.org. Do a search for arborists in your state. Good luck.
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Mike LaMana, MS, CTE
Consulting Forester & Arborist
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