She "controls" her husband by doing both
...That's the bottom line, but...
Being a site about hermeneutics, "how we got here" is the important part to include in this answer.
I. How to think through this
This is largely a question about opinion. The Bible doesn't specifically state an answer, nor does the Bible assume that we need to have an answer. It's a great question, just remember where it fits.
Your question tries to use "non-Bible" types of behavior to describe a character in the Bible. Technically and by definition (viz 'behavior'), this involves "psychology". So, we might need to use that as a keyword in our research. "A woman who encourages" or "a woman who mistreats" could show up in psych or "people skills" research, but they could also be argued from Paul (Ephesians 5:33) or the "Proverbs 31" woman or the "rooftop" woman (Proverbs 21, 25). While those Bible passages provide insight, and Bible should be our main framework, they don't answer as much as your question asks.
Ephesians 5:33 (NASB) emphasis added
Nevertheless, each individual among you also is to love his own wife even as himself, and the wife must see to it that she respects her husband.
Proverbs 25:24 (NASB)
It is better to live in a corner of the roof
Than in a house shared with a contentious woman.
Proverbs 21:9 (NASB)
It is better to live in a corner of a roof
Than in a house shared with a contentious woman.
- Since the answer will be largely opinion, we need to test and see how well our answer works in understanding other parts of the Bible and especially Jezebel's story.
II. Answering your question
Her question is "rhetorical", as you say. Of course Ahab is the ruler of Israel! Her question is not respectful; she doesn't talk to him as if he respects himself.
She makes everything better for him by taking charge herself. That is when he gets "merry" and happy, like a little boy whose mother made an ice cream sundae for him.
With these two together, Ahab seems to be more of a "mamma's boy". That gets into psychology and relationships, which is part of what your question is about.
A. The Oswald Chambers approach: Psychology from the Bible
Asking what kind of wife Jezebel is also falls under the large topic of "psychology". The Bible often connects with this. Consider the acclaimed Oswald Chambers and the book he wrote while he was alive: Biblical Psychology: Christ-Centered Solutions for Daily Problems
Look for similarities to Jezebel in these three pop-psych articles:
I feel more like a mother than a wife
...Honestly, I feel more like his mother than his wife. We both work and I still do the majority of the household chores and look after the children.
He complains about being tired and doesn’t take the initiative to do anything. I mean, he doesn’t even bother to think for himself half the time, and when problems arise I am the one to find the solutions.
Marriage, men, and mother syndrome
The wife is angry and complains that she has to do everything for her lazy husband... If this sounds familiar, help is here in the form of an in-depth guidebook called How Can I Be Your Lover When I’m Too Busy Being Your Mother: The Answers to Becoming Partners Again.
33 Ways People try to Manipulate You
33: Acting as if they were above you
32: Condescending comments/tonality
17: The free lunch “No strings attached”
16: Overly complimentary
15: Loaded questions
10: Trying to exploit your weakness against you
2: Make you believe it was your idea
That seems a lot like Ahab and Jezebel. But, remember, Jezebel came before pop psychology.
We might use Jezebel to interpret psychology, not merely psychology to interpret Jezebel.
Since you're asking to apply psychology-related traits to the Bible, half of the research involves becoming familiar with psychology.
Do more research on your own or consult the IPS site from StackExchange. Doing psych/interpersonal study here would get off track from hermeneutics. Let's look more at Jezebel as a Bible character...
B. Interpret Bible with Bible
Look just a little earlier in 1 Kings, when Jezebel and Ahab get to deal with Elijah the prophet rather than Naboth the farmer...
1 Kings 19:1-2 (NASB)
Now Ahab told Jezebel all that Elijah had done, and how he had killed all the prophets with the sword. 2 Then Jezebel sent a messenger to Elijah, saying, “So may the gods do to me and even more, if I do not make your life as the life of one of them by tomorrow about this time.”
...She's a murderer, having killed Naboth (1 Kings 21:8-14) as part of how she got the vineyard for Ahab. She also tried to kill Elijah for threatening her power.
Considering how she both mistreats and encourages her husband the king, the rest of her actions indicate her motive: control. But, we still can't come to a conclusion yet!
C. Church teaching
Using a Biblical framework, look at what many Christians call a "Jezebel Spirit", which gets it's name from Revelation 2:20.
Revelation 2:20 (NASB) emphasis added
But I have this against you, that you tolerate the woman Jezebel, who calls herself a prophetess, and she teaches and leads My bond-servants astray so that they commit acts of immorality and eat things sacrificed to idols.
What is the Jezebel spirit?
One trait is her obsessive passion for domineering and controlling others, especially in the spiritual realm. When she became queen, she began a relentless campaign to rid Israel of all evidences of Yahweh worship.
12 Warning Signs That a Person is Under the Influence of a Jezebel Spirit
- They target the headship. They offer free help to be their top assistant because they want their protection. It hides from the leader’s view but manifests in front of others.
Jezebel resorting to murder whenever her control is threatened, while both condescending and encouraging her husband the king at the same time, indicates that she is the de facto ruler of Israel. She is the puppet master and her husband King Abab is her puppet.
That conclusion comes from a mix of Bible, pop-psych, and Church teaching. It has opinion and non-Bible ideas (because you're asking how to apply the story outside of the Bible, which is good.) We only know if that conclusion is good by applying it elsewhere as a test while always asking this question:
Is that interpretation 1. consistent and 2. helpful in understanding the rest of the Bible?
Here are the three areas we looked at here, which you could continue much more of on your own:
Pop psychology and codependency-manipulation issues in marriage (non-Bible; the 'application' part of your question)
The rest of the Bible story in 1 & 2 Kings and Revelation 2:20, where she is mentioned by name; also consider Deborah in Judges 4-5, Ruth, and Esther for contrast (Bible)
"The Jezebel Spirit" (Church teaching; very relevant, same name, cross-denominational)