One point of clarification, the I-130 is not a visa of any kind. It is a requirement for a family-based visa, but it is not a visa in and of itself.
I would just apply for your ESTA. I've travelled to the US, and renewed my ESTA while I had an I-130 approved and was waiting to process my immigrant visa. If your ESTA is approved, you'll likely just be fine—just go for a short trip, and be prepared to show that you have continuing ties to the UK.