I eventually found the answer to my own question. I had 2 problems. Turns out, if your weir coefficients are too high, as mine were, it wall cause model stability problems.
Secondly, if you rename the ‘River Name’ or ‘Reach Name’ on the upstream (HW) side of a lateral weir, the lateral structure will stop working. The software will calculate an amount of flow that should pass over the weir, but that flow will remain in the HW river reach, and will not appear in the TW river reach. If you rename the River/Reach back to what it was originally, the lateral weir will work again. The River/Reach on the downstream side of the lateral structure can be renamed without affecting the flow split results.