If you're generating some truly-random "password", I'd call it a key instead. Just a minor terminological note.
Anyway, while that split-the-key scheme works, I wouldn't use it over one of the real secret sharing schemes cryptographers have developed, e.g. Shamir's secret sharing scheme [1]. If you just split a key and give pieces to different people, the more pieces of the key an enemy can collect, the easier time they will have when brute-forcing it.
On the other hand, Shamir's secret sharing scheme is an information-theoretically secure threshold scheme. That is, a key is broken up into n pieces and t of those pieces are required to reconstruct the secret. In Shamir's scheme, the enemy can collect t-1 pieces of the secret and still have no chance in reconstructing the password; it simply is impossible.
The scheme works off of the idea that an m-degree polynomial is uniquely defined by m+1 points. For example, here's a point from a 1-degree polynomial (line), which would model a t=2 scheme: (1,4). Can you figure out the y-intercept? (Actually, Shamir's scheme uses finite fields, but I think asking this question drives the point home.)
So, generate a key, split it up into a bunch of pieces, and require a threshold of those pieces to be present. Coercion-free and even if an intelligence agency can compromise many pieces, they still can't do anything until they've hit the threshold. Also, if you want to require all pieces present, just set t=n.
[1] https://en.wikipedia.org/wiki/Shamir's_Secret_Sharing