A sub panel should not have the neutral and earth ground bonded. They
need to be separate.

Yes. There is nothing "neutral" about a neutral. And why it is that if there are only three wires from the House (Main) panel to the sub panel, an additional SEPARATE ground must be provided in the Pump House, as that third wire is now, de-facto, the neutral.

As it happens, there is no reason not to have multiple GROUNDS within a system, as long as there is one, and only one Neutral. I remember back in the day the master-electrician I worked for was a fanatic about balancing loads as closely as practical, even in a residential application. If loads are exactly balanced, then from the Panel to the Pole, the neutral will carry no current at all. But within the residence, pretty much every neutral will carry load. Easily demonstrated with an ammeter.

Peter Wieck
Melrose Park, PA