My main service panel is installed in a detached garage. Our new home is fed by a subpanel run underground from the garage. At the garage panel I have two ground rods and the neutral bar and ground bar in the panel are connected.

At the house subpanel location do I need additional ground rods and should the neutral and grounding panel bars be connected as well ? Thank you.

Since the house is in a detached structure from the feeder, there should be a ground rod at the sub-panel. Neutral and ground busses should not be connected together at the sub-panel.

Actually it depends on the feeder if the grounds and neutrals should be isolated.

With a "3-wire" feeder the grounds and neutrals are bonded just like in a main panel.
With a "4-wire" feeder the grounds and neutrals are kept isolated.

My feeder is 4-wire so I would take it that they should be isolated. Are you both in agreement on the need for a separate grounding rod ?

Unfortunately I'm not sure that I agree with StanFortyMan's statements regarding the 3-wire and 4-wire feeders. I've never heard of that rationale. The basic point that 'Keep it Simple Stupid' made, I'm in agreement with... that the neutral bar and ground bar are kept separate at sub-panels. The NEC only requires bonding of the neutral/grounding bars at the main service panel to eliminate multiple ground paths. I am open to being re-educated on this matter so anyone please feel free to point me to the articles in the NEC that mention this 3 wire/4 wire feeder rationale for bonding the neutral/grounds at the subpanels.

Jpen, it is not my "rationale", it is in the NEC.
Please see 250.32(B)(1) and (B)(2).

This was changed in the 2008 NEC to not allow "3-wire" feeders (250.32(B)(2)) any more in new installs.

But does a 4-wire underground feeder require a ground rod at the main panel? I would suspect the answer is yes. With the ground and neutrals remaining unconnected at the main panel, this would make sense.

ALL "main" panels/disconnects require a grounding electrode.

ALL sub-panels at detached structures require a grounding electrode.

This has NOTING at all to do with the grounds and neutrals in the panels. A ground rod is completely unrelated to either of them.