It should be super easy. The trick is...don't try to use the "restore" option, which will prompt for your seed (FYI, NEVER type your Trezor's mnemonics into any computer--EVER--unless your trezor is lost/broken). What you want to do is simply repeat what you did to set up Electrum-Dash with your Trezor on your home computer the first time. Choose "new wallet" and just enter your pin. Electrum-Dash will then get the master public key from the Trezor and rebuild your Dash HD wallet tree from that. It won't actually be a "new" wallet. It is simply another copy of the same wallet that you have on your other Electrum-Dash with your Trezor.
There should be no problem running multiple instances of HD wallets. Just be careful not to use the import/sweep private key function, because those can only be stored on the local computer and won't carry over, as they cannot be determined from your Trezor's seed.
Thank you - that's exactly what I needed to know!