Since m/44'/0'/0' worked and the code you gave above, I think it goes:
m/44'/client_id'/0'
(either that or m/44'/0'/clientid'/0' -but that may be less likely)
How do you know the addresses generated have actually been funded though? I think you need a script thst goes through and checks from an api (such as a block explorer) as to whether an address you control has been funded or not.
The problem is that m/44/2 is litecoin
The third level will go to different altcoins. I don't know how to handle that (an altcoin path) in a bitcoin wallet.
Just take a look at iancoleman and you will see.
It's just replay protection and there are tools to convert litecoin public keys to bitcoin ones and vice versa (they just add an offset to the public key to make it different - the private key will be the same).