You can use the RX out jack for the HL2 if your radio has one. Solves the TX into your SDR problem easy.
Be sure the HL2 TX is disabled though, or better use the Aux RF jack on the optional HL2 IO Board or equivalent connection inside the HL2 on the io header for Rx only so you do not TX into your big rig Rx Out port.
On radios like the K3 with 1st stage buffered IF output for a panadapter, can hook that up to the HL2 rx ant port and never worry about tuning except maybe for slight changes due to mode offsets.
Thetis has 4 CAT port setups, no idea how to use them. Will have to read up on those.