Unless you're going door-to-door and killing whole families, there's little you can do in a single day to actually shift your alignment that much, especially from one end of the spectrum to the other.
If you consider some 100 point scale where 100-68 is Good, 32-0 is Evil, and everything in between is Neutral, you will almost never do something that is worth even 5 points either way.
>They ran into the Redbrands, killed most of them and tied up one of them after beating him within an inch of his life.
This is fine. People die in mortal combat. They were presumably trying to kill the PCs as well, and one can never ensure they don't kill anyone in a big melee with swords and arrows everywhere.
>barged in the door traumatising her kid for life
This means nothing.
>interrogated the bandit with a knife to his throat
This doesn't really rise to the level of Evil. Threats and promises of violence used to force compliance aren't the same as, say, torture, which is Evil.
>dragged the bandit back to the town square, executed him while he was pleading for his life, and hanged his body using his cloak to put him on display
This is Chaotic. The party decided they were the best ones to interpret and enforce the law (though "Lawfulness" and "the law" aren't the same). They took matters into their own hands when things were already under control. The execution and display is just tacky, but doesn't really rise to Evil, provided it was performed humanely. He was a baddie, after all.
>Mechanically there will be no consequences since the paladin didn't take his oath yet
Mechanically, Paladins don't have to remain Lawful Good anymore. They just have to avoid egregiously violating their Oath, which can be served a number of ways, and not all of them Lawful or Good.
Remember, alignment shifts happen over a long period of time. Over the course of an adventure, you're not going to see someone drop from Good to Evil unless they are making a conscious effort to be a shit.