This is really off-topic for this forum. I would probably repost in the House Plants Forum, linked below.

Here is a link that might be useful: House Plants Forum

What the heck, I'll give you my opinion. I mean what's the worst that can happen?

I would be inclined to cut all the tallest stems with a sharp pair of secateurs when your wife is not looking, leaving the two shortest stems so that some leaves are still on the plant. When the cut stems have produced more branches and leaves, you can tidy up the lowest two branches if you think it would improve the look of the plant.

Can you put your umbrella tree somewhere where it will get more light? Not direct sun, but a very well lit place where your wife never goes. She might have a fit but I am certain that it will branch nicely after being trimmed.

I would cut the (tallest) stems at the height of the bottom of the picture that you have on your wall.

Schefflera is the name of your plant.

I am not sure how long you have had the plant in your home. If it starts to look unwell, it will almost certainly be due to lack of light.

Your tree has a very distinct growth cycle, during which it's ability to turn light energy into food waxes and wanes. Where you live has a significant impact on what you can reasonably do, but cutting your plant back now might seem reasonable to a person, your plant would certainly not look at it that way (if it could). It would say, "Hey - how about this for a deal? Tell your wife you'll cut me back in June - around Father's Day (which nearly coincides with the summer solstice - an important time for plants). Tell her I need to have that late spring warmth and sun to put away a little stored energy, and I need to be in a part of the growth cycle where my ability to covert sunlight to food is optimal when you start whacking at me - that way, I'll recover very quickly and still have time to put away some energy reserves for NEXT winter.

IOW, if you learn to work WITH your plant's natural rhythms (do a search for endogenous and Circadian rhythms) instead of against them, life will be easier for both of you. Of course, that whole happy wife - happy life thing just might trump the best laid plans.

Your plant has the unwell look of one suffering from severe root congestion - all growth concentrated in immediate area of apices (growing branch tips - apical meristems), so a repotting (much different and more involved than simply potting up) should be part of your plan, probably preceding the actual pruning by 2 or more weeks.

C'mon over to houseplants or the container gardening forum & we'll put together a plan that all 3 of you will approve of.

By paying attention to details, you can take a scheff (this is a more compact plant than yours) looking like this in Michigan

to looking like this, in 3 weeks. It's back-budded heavily, as you can see.

And that plant was shipped to Boston or NYC (I forget which) during that 3 week period. That's the new owner .... and there's an interesting story behind that whole deal.

Al