Haplok: A lot of good advice.
But one method of reliably auto-tripping is missing: bite attacks and Cloak of the Winter Wolf (available as early as start of Act 2).
You'd probably want to start with a Motherless Tiefling, as that's a permanent free bite attacks.
But you can actually get more and they stack (whether intentionally or as a bug)!
1. Vivisectionist can get a bite at level 2 with Feral Mutagen Discovery (as well as Claws, 4 max AB attacks with sneak attack damage bonus at that level are just insane, particularly for a Strength build, who doesn't need to care about dex to damage bonus). At level 4 mutagen lasts 40 minutes already, which is enough to carry you trough most locations (and you can get some more Discoveries with more levels, like resistance to critical hits/sneak attacks). I actually like to take at least 12 Vivi levels for the Greater Mutagen, Improved Invisibility, Echolocation, Haste, Shield, +5 Nat AC Barkskin (and Trips will benefit both from Str and Dex bonuses it can offer).
2. Dragon Disciple gets a bite attack at level 2 (contrary to PnP sources, its permanent here). Again the bonus Str from 4 levels can be put to good use. Bonus AC and high HPs won't hurt either. You also get a free feat at level 2.
You need another class to qualify though. My pick is Archeologist Bard. With 2 levels you get Uncanny Dodge, which is very useful in Kingmaker, particularly end-game. If you already have 10 levels of Vivi you can get Opportunist as your bonus Bard Talent. Also with Archaeologist 2 / DD 4 you will be able to cast Mirror Image, which is a great defensive boon. Plus you can use a luck boost to many stats for a few rounds per day.
3. The we have Barbarian, who can get Beast Totem powers as his Rage powers at level 2. They are active only while raging. Having a 4th Bite attack (and trip attempt) would be nice, but a Barbarian is not compatible with monks alignment wise and I want those monk defenses, so personally I skipped it.
Your Artisans (Varrask maybe?) can also deliver you a breastplate that lets you cast Aspect of the Wolf 1/day. It lasts for 10 minutes AFAIR. Not very long, but in general investing in Druid/Ranger mainly for tripping is not worth it IMO.
But your fauchard weapon choice for a tripping machine was spot-on!
Mid game Serpent Prince is the best damage dealing weapon (unless you metagame and get certain end-game loot very early, then it's more like... second best).
But late game (Act 4 in my case, but I got lucky), Sahiya can make the +5 Mastery fauchard for you. And it's crazy in combination with a tripper. It offers +5 CMB/CMD, grants Freedom, makes you immune to enemy trips and bullrushes and most importantly, it deals normal damage whenever you land a combat maneuver.
So say, you have 3 Mastery fauchard attacks (maybe 5 if hasted and with Transformation spell), then 3 bite attacks (probably with sneak damage bonus, if you went for Vivi). Each bite attempts a trip with the Cloak of Winter Wolf and when you succeed, Mastery deals its damage to that enemy too (no attack roll!). The caveat is that you can't trip an enemy who is already prone, but if you manually switch to another target in range, you can trip up to 3 enemies in a round (and deal double damage to them too). If they survive (a big if), when they get up, they will obviously provoke an AoO from all allies in range too. More is of course possible, if you for example trigger Aspect of the Wolf from the breastplate. Or went Barbarian too.
Note Mastery also allows you to damage enemies you can't reliably hit due to inflated ACs (like the dragon) if you can beat their CMD, as the regular (non-bite) Combat Maneuvers ignore AC. Of course this means only 1 attacks per round (plus AoOs), instead of 7-11.
Most notable buffs are Legendary Proportions (+6 Str, +2 size bonus to CMB) and Transformation (gives full BAB, but it's a level 6 spell for Vivi, so would need 16 Vivi levels, a short effect can be gotten from an end-game longsword from Nazrielle). A bit of a trade off there - do you want permanent bonus bite attacks and trips and boosts with Dragon Disciple or level 6 spells from Vivi - where Transformation would temporarily offer +5 AB and an extra regular attack (plus Grand Mutagen, which kind of balances the stat DD boosts - less Str, more Dex and Con).
bite forces you into 5ft melee, so reach from fauchards will be useless. AC of about 50-ish is doable on str 2h melees, granted you abuse monk stuffs, but I don't think this is what he had in mind.
Also afaik bite attacks are limited to 1 per round no matter how many sources of that you have by pnp rules at least. Never bothered to test how it works in this one.