If you have reason to believe the back is significantly different from the front then you should test them separately. Yes, you would have to pay for both.

Ideally you would pull multiple cores from each area you want tested and that would get you an "average" across the area. This is to avoid a situation where - and this is a crazy example - you dumped a bunch of lime in one spot and your test comes back with a high pH but the rest of your yard is actually acidic.

Thank you! Is the best way to get the dirt to dig/lift up a piece of sod and get it from underneath there?

That's usually what I do. Technically, you want a sample comprising everything from just under any organic layer (at the top, thin, and usually dark brown) down to the full four inches. Barring a soil sampler, just getting it from the sod down to 4" is usually the best you can do.