Should I get my own second inspection separate from the builder's inspection on new construction?

Yes. Bring in an independent inspector you hired yourself, every time. Start with one question: who performed that first inspection? If the builder arranged it, you're relying on the builder's own team to catch and flag problems with the builder's own work. For a couple hundred dollars, an independent third-party inspector gives you a set of eyes with no stake in the sale confirming everything actually works before you close. New construction is not automatically flawless. Systems get rushed, punch-list items get missed, and the person most motivated to spot those things answers only to you. Schedule the inspection with time left on the calendar before closing, so anything it turns up can be fixed by the builder or negotiated, rather than becoming your problem after the keys change hands. On the largest purchase most people make, that's cheap peace of mind.