Can I play Emperor's Divide at Vilemaw's Lair to move my units back to base?

No. Vilemaw's Lair's restriction ("Units can't move from here to base") overrides Emperor's Divide's move instruction, so your units stay put.

The spell resolves and does nothing for those units — instructions that can't be followed are ignored (Rule 359.3.e.6). This is a hard restriction: no spell, ability, or Standard Move can move units from Vilemaw's Lair to base. Recall effects still work, but movement doesn't.