How to reliably prevent multi-accounters from putting his/her Pokemon in after kicking out a Pokemon in the gym using secondary accounts?

Here it’s more than just that.
Hardcore groups of 6 blue with alts in other colours (edit: actually family members sharing accounts) occupying the same gyms at the same fixed timing every day, and using 3-round sync attacks to evict “stranger’s Pokemon” if they somehow manage to get in.
These aren’t the average players, they know type advantage and raid counters, and some of them have even duoed Deoxys! They also read this site and TSR, so I can’t say too much.

They sometimes take down a full blue gym, place a trash red/yellow mon, and change it back to blue. Or they will just use sync attacks and the traditional 10-minute shaving method, if anyone feeds berries. They also know how to battle the defenders at the back 3 times while only battling those in front once. Also, using type advantage and charging up a full charge move to instant kill the defender as soon as the battle starts, reducing the window for the defender to feed GRBs.

Back when network errors in gym battles after raiding was still a thing, these gym hoggers even used alts of a different colour to raid literally every raid at their gyms (except some T4s), and when their gyms get attacked, enter the battle with these accounts to disrupt the attacker(s). And some of them live on top of gyms, which makes it even easier.

Best part is, if a stranger’s Blissey enters, 5 trash mons will follow, and they will grind down the blissey.

If your facts are as stated I have 2 things for you to consider:

1) If she is making the Gym stronger THEN make sure you put in a good defender and keep it motivated via berries so you are not the one getting kicked out.

In some sense, I get this frustrates you, but the opposite is also frustrating. You put a good defender in a gym, because you want that gym to last, or working on gold, and some idiot on your team comes by and drops in a pidgey. In that sense I'd happily root for that person to kick out that pidgey and throw in a Chansey because now my pokemon is more likely to stay and ward off.

For people who view PMG as a territory game or a Team vs Team game, I don't mind those actions on my side getting rid of the trash people put into gyms.

Gyms in general need a revamp in the system