She has pretty much two thematic anchors in her lore: she's a cop and she's a sniper. And while the second one is realized at least a little bit in her ult, the first one kinda feels like back then it was an excuse to give her a skin that looks like the stripper-version of a modern day police officer.
In general she's a more or less normal person who uses her smarts and several gedgets (like her personal rifle which was a present from her parents) to catch ciminals in Piltover.
And here we run into our biggest problems: her main function ingame is sieging towers, but while that works with champions like Jinx, the "towerwrecking" aspect just looks weird on her, ESPECIALLY if its one of the reason you pick her. Visuals aside, the very idea of a cop running around and breaking stuff is weird.
Almost as weird as that a cop runs around killing people. Shooting someone in a trap looks more like an execution than anything to me. I'm not sure if you americans have a weird sense of what a police force is supposed to be and do, but KILLING PEOPLE IS NOT THE JOB OF A COP. In fact, it's the absolute opposite of that, as their job is catching the criminal and putting him to the justice system so it can do its work. And in a game about people literally killing each other, that's a weird problem to solve.
The only way to solve this would be to make her more of an "Utility-ADC", who might deal less damage than other champs in the class, but makes up for it with the various tools at her disposal. Especially the "gadet"-part of her theme might work here, altho right now it is slightly poorly utilized. Her net feels like a close combat tool, completly misplaced in a sniper-kit, and her traps are just absolutely barbaric to say the least.
In-game Caitlny should play like a champ who CAN be a extremly dangerous sniper if she wants to be one, but who's strenghts are not limited on it as in comparision to Jhin who is 100% about murdering people with everything he got.
So her kit should more look like this: 3 utlility/farm spells and the ult that is a version of the Jhin ult. How it could work: when casting the ability she roots herself and the cam zooms out, but her area is a bit less wide than Jhin's. To make up for it her shots are faster and have special effects: After casting the ultimate the ult and the basic spells are replaced by "special shells" that all have different effects on usage:
1.) "Light's out": champion and close enemies hit becomes "near-sighted" (think of Quinn Q) on impact (low damage)
2.) "Heavy Hitter": Slows champion hit. (low damage)
3.) "Shocker": champion hit is stunned and AoE around them is damaged. (moderate damage)
4.) "Last Resort": Pierces through all enemies hit, completly ignores armor and resistances on the champion hit. Bonus damage to targets that are restricted in their movement (Ya Dead)
As for the rest of her kit: the only way to get some power into there is to reduce her range. And so: Cait gets a secondary weapon and only pulls her rifle for the ultimate, and instead utilizes another, more suitable tool for close combat. I'd propose some sort of "Stun Gun", but not a hyped-up version that Jinx uses, just to bring her back in line with other adcs and allow more ineresting abilities:
Her abilities could look as follows:
Part 1: Tracking: you can see tracks of enemies on the ground when they are not in the vision of your team, they vanish after a minute.
Part 2: The first basic attack with the stun-gun or Q to an enemy stuns that enemy. Only works within X second on the same enemy champion.
"Perfect Aim": Charges the Secondary weapon for a short time, during that time you might point&click on four targets. They are all shot when the charge ends. Damage dependes on charge time, minions are executed at some point. (Like a weird version of McFCree's High Noon for those who know this skill from Overwatch). This is kinda supposed to be the "farming skill", kinda like Jhin's Q is.
"Flashbang": Pretty straightforward, it's a toned down and less lethal version of Heimerdinger's grenade that, while it doesn't stun, it does slow and near-sight the target.
"Portable Police Barrier": Throws a projectile that lingers on the ground for a short moment before unfolding itself into a barrier that prevents movement and dashes through it. It can be destroyed by basic attacks however, just like Yorick's barrier. I'd propose to put it on a charge system, the range of it scaling per level. Also, for the officer skin I'd give it this yellow tape "POLICE LINE DO NOT CROSS" look that you see in movies sometimes ^^
With a kit like this she'd be more of an utility adc, kinda in the category of Ashe and Sivir. With the range and the countless traps gone she'd be a LOT less frustrating to play against, but she also has impactful spells that make her noticable and fun to play, the most unique aspect being the Protable Barrier that can be used for self-peel.
With her ultimate she's still a sniper, but even there the "utility" aspect shines through. Set yourself up in the back behind the teamfight with your barriers, and then see who needs what in the fight. Your APC needs peel? Give them the "heavy hitter" or the "shocker"! The enemy is stacked onto each other? Blind them all with a well aimed "Light's Out!". And if nothing works, you still got your lethal "Last Resort" to show your enemies not to mess with the police-force of Piltover!
But apart from her sniping, the main reason she is picked should be her utility: using barriers to lock down the river before a dragon fight? Sounds awesome to me! Knowing you run into a bush with 5 enemies in there because you can see the tracks towards them? There's no other champ who can do that! Amazing utility combined with useful cc make up for a versatile champion who can easily keep up with the other marksmen, while being a lot less frustrating to lane against!