Inserting a two-page spread into Indesign

Question

I have a document with three two-page spreads.

I want to add another two-page spread between pages 1-2 and 3-4, so I chose Layout > Pages > Insert Pages to add 2 pages after page 2.

As shown above, the first spread now contains four pages. How can I break that into two spreads with two pages each?

I've seen posts that say to select the errant pages (3 & 4 in this case) and to choose "Allow Document Pages to Shuffle" from the Pages menu. I've tried this with various pages selected, also tried this while unselecting the "Allow Selected Spreads to Shuffle" option, messed with the File > Document Setup > Facing Pages checkboxes, but I've been unable to create the desired layout which would be something like this (mockup created using Photoshop):

Answer 1

Simply highlight the 2 pages in the Pages Panel and drag them until you see a solid, straight line. Not a bracket line with hooks on the ends, a straight line.

The Allow Document Pages to Shuffle is somewhat illogical. Whether or not the check mark is next to that item doesn't necessarily mean anything.

What matters is... if you are trying to do something with respect to moving pages, and the panel won't let you, then you want to toggle the Allow Document Pages to Shuffle option... that may or may not mean the check mark is next to the menu item. But, the check mark doesn't really matter, it's inconsistent.