My wife is the first one who reads my writings, and I'd like to keep her in the dark until I have a solid draft to show her. But I need a second set of eyes with my plot too. If I showed her my plot and asked for her help in choosing plot paths, would that jeopardize her role as a beta reader?
Your wife is actually an "alpha reader". She understands you, she understands your goals, she is a springboard for ideas, and as your life partner she is invested in your happiness and success. This makes her far more important to you than a beta reader.
Your beta readers should probably be kept at a distance from the project so they can approach your writing without pre-knowledge of the structural and character compromises you had to make. Your beta readers will bring their own pre-conceptions about stories and who they believe your characters are and how they "should" behave. The opinions of beta readers are not "right or wrong" they just are, and hopefully articulate enough for you to gain valuable insight into the range of people who will have varying opinions on different parts of the story.
A wife is more important than a beta reader.
Don't downgrade your wife. Find some actual beta readers, and more than just 1.
If she knows the plot already, she won't react to it the same way a first-time reader would, so yes, it would definitely jeopardize that role. If you really need some advice with the plot, you could show it to someone else trustworthy enough, or maybe make someone else your beta reader, if possible .