Summary (TL;DR): How do I murder a tree and make it look like a suicide? :)
Mrs. MacNerd here (hoping Mr. MacNerd doesn't read this!).
I live in the jungle in the middle of the US. I actually live in a subdivision, but there's no way to know that if you saw pictures of our yard. The reason is Mr. MacNerd is nearly incapable of pruning/weeding/thinning plants. (I kid you not! He allows weeds to grow so tall in our garden they block the sun to our vegetables!!)
Our walnut trees have proliferated, because squirrels constantly bury the walnuts. I sneak around and saw down a walnut tree here and there every so often while Mr. MacNerd isn't looking.
But one walnut tree is growing three feet from our house! I measured! I managed to trim the branches that were hitting the house while Mr. MacNerd was away for a few hours. But he will have a cow if I cut this tree down. He claims it shades the house. We have many, many trees shading the house, and we don't need another. How do I make it look like this tree died of its own free will?
If it were not a nut tree that animals or god forbid, humans may eat, I would recommend this:
Get a long 1/2” or 3/4” wood bit and a (preferably cordless) drill. Drill into the base of the tree at a steep downward angle, as far as the bit will go. Two or more holes are better than one. Get a powerful concentrate of triclopyr herbicide like Remedy which is 60% triclopyr. If you can't get that use Bayer or Ortho Brush and Posion Ivy killer which is 8% triclopyr and hope for the worst (for the tree).
Fill the holes you just drilled to near the top with Remedy (or substitute) AND SEAL THE HOLES WITH CAULK. Maybe put some bark on the caulk to camouflage the caulk.
In your case though, you need to man up. Ask your husband if one tree is worth the thousands of dollars in foundation damage that it is likely to cause to your house.
Google up some photos of foundation damage from trees and you may get hubby to wield the chainsaw himself.
One note. If the tree is already very large, killing it or cutting it down may do as much damage as leaving it. As the dead roots rot under the house foundation, the soil subsides resulting in foundation damage. Damned if you do, damned if you don't.