How do hardware wallets integrate with software clients/nodes?
Sadly there is no standard yet.

But a wallet standards group is being formed and some meetings are planed (april 2017).

At the moment, each hardware wallet provider writes plugins for wallet-apps which is a strange development direction.
There are Trezor/Digitalbitbox/Ledger plugins for Electrum and Copay,... but the plugins are in the source code bundle of the corresponding wallet-app provider, leading to the problem, that the hardware wallet provide has no direct way of fixing bugs or even improving the plugin.

A standard would be the right direction.