yoga is meant to be done on an empty stomach. Something like no food for 2 hours before hand.
For the OP i'd say it's more important to get the shake in asap and do yoga some other time. I've done it before bed and it's very relaxing and helps me sleep well. You're probably doing more intense yoga since you say it's more of a core workout so that might not be the best before bed.
I found core yoga didn't do much, i just like using it to get a good stretch and relax.