Talk to your DM. I've said this story multiple times but look at the contract and the other store you are going to work for.
My pharmacist at CVS was offered management position at Sams pharmacy downtown. The DM said it wasn't a conflict to work at CVS part-time because they weren't direct competitors and they were farther away. If it was the sams down the road however...yeah, conflict of interest.
RA and then Wags or CVS though? Yeah, doubtful...