Theme (and Tone)
Theme is a creative tool during the creation process, plotting and first draft.
Tone is a creative tool in the refining process, second and final drafts.
Horror and Comedy are about Theme and Tone – more than other genres because they can't rely on tropes. (They have tropes, but as they become familiar they stop having the intended effect.)
Instead Comedy needs to be funny, Horror needs to be scary – both need to hit visceral, primal emotions that (at times) supersede logic. It's more involved than just 'Hero Has a Bad Day'. Comedy and Horror go by their own story rules.
Character and Plot – the most important parts of other genres – are derailed, pushed to breaking limits, and beyond. Extra suspension of disbelief will be allowed in service to the theme. In fact the great moments are probably when they 'transcend' reality, that is when they seem to hit it.
My suggestion is that you brainstorm on your Theme as this is going to answer some of your big story questions.
Tone is... an ongoing exploration of the writer's craft. Mostly you just need to get out of the way and let the story happen, especially at this early phase.
How to Theme for Horror
You need a big arc that drives smaller story beats that reveal a pattern. For Horror it's aways a negative arc.
In general, Horror is about reducing the MC's agency and options. Mistakes are made, equipment is damaged, territory is lost, safety nets are removed, valuable people are injured and die... Reduce, reduce, reduce.
Each story beat is a loss and this starts right away, but typically the protagonist does not see these early beats as losses, rather these are 'challenges' which are 'solved' (badly). The cost is high, the compromise is more than planned. Every situation has a negative spin. Other characters become uneasy. This will generate unbalanced tension in your story, readers know this can't end well.
The MC actively makes choices (or compromises) which lead to them being increasingly isolated, trapped, un-helped, or disbelieved. Red flags are ignored, repairs are postponed. When these decisions come back to bite the MC later at a crucial moment, it feels like a payoff and inevitable.
Meanwhile, your horror-premise is chiseling away at the edges of the narrative. The influence is plausibly deniable at first, but will rise (or be uncovered) in stages, eventually overtaking the story. Protag is coping with a downward arc and losing agency while the horror-element is unfairly altering the landscape – it doesn't need to be supernatural, but is probably always exaggerated.
The tipping point will act as a plot twist that wipes out entire story goals. Characters will completely change under unnatural circumstances (maybe not all at once). An MC who has been established as 'coping' may have less to lose, be more adaptable to loss and sudden change, straddle parts of society, and find a new zeal for life – whereas a more comfortable character might stay in denial longer and be slower to react.
Compare to:
Tragedy where the hero creates his own undoing, making several wrong moral decisions away from the 'good' path.
Melodrama where the MC endures injustice, power-imbalance, and abuse to generate sympathy.
Dark Fantasy Heroic fantasy with horror tropes.
Horror vs Terror
According to a 200 year old writer's debate, the principle elements of Horror genre are subdivided into 2 emotional states: horror and terror.
Terror is about anticipation, suspense, adrenaline, thriller, the fear of what will happen.
Horror is about what has happened. It's more cerebral, gothic, revulsive, un-reconcilable, look at the ugly consequences.
They can be reduced to primary survival instincts. Terror is an instinct to flee from immediate threat, while horror is more the awful awareness of an abnormality or corruption: OMG, something is wrong!
Adjacent negative primal emotions that could be woven into your theme might be disgust, vengeance, shame, or morbid grief. Leaning heavily on another brutal emotion can enrich the tone, add layered motives, and justify obsessive sabotaging behavior that will defy common sense but progress the arc.
I think if you are clear on what is driving your MC, you can see their motivations and write their choices. If you have an ensemble cast each might have their own negative motivation and fate.
Some suggestions
Your broad strokes include a Father character who took this journey before her, and failed. This gives a lot of opportunity for foreshadowing her fate, but also the chance to walk in his shoes and examine any gruesome choices he made, seeing them now in a new light as she faces them too.
She might perceive her downward arc as a mystery to be solved, or an obligation to un-shame her father, or to redeem herself (proven better than her father).... She will understand this goal early on in a naively positive way, but part of her downward arc will also be the corruption of her original goal.
She will be unpacking her feelings about her father along the way, somehow this is not possible if she just stayed home and had therapy. I said horror is not character-driven, but the MC doesn't know they are in a horror story. She will think as a literary or genre protagonist until the horror robs her of her last illusions.
Needless to say, she should make discoveries about her father that don't match her image of him, and her feelings will evolve as she gets closer to the truth.
Happy ending or not?
Every story starts and ends on a status quo. Horror does not need a solid (reliable) status quo at the end, but it does need a resolution.
The Theme can end, even if the horror-premise is left unresolved.
The Thing (1982), original story by John W. Campbell Jr
The plot is a shape-shifting monster from outer space, but the theme is suspicion and distrust between the men.... The story ends not when there is 1 man left and the monster defeated, but with the last 2 men freezing to death locked in a faceoff.
In Rosemary's Baby, Ira Levin
after uncovering the conspiracy of her pregnancy, she stays to nurture the baby.
The Stepford Wives, Ira Levin (again)
the protag suspects local women are being replaced with compliant facsimiles. She is ultimately replaced, as a new woman moves to town. The cycle continues.
Plot and character resolution are superseded by a pure-theme ending. The story ends when your MC reaches the ultimate conclusion of the story's theme, the abnormal or corruption to the nth power, no longer an uncertain fear but pushed past the limits of reality.