I'm having trouble powering my boards altogether. Right now, I'm using 8x AA batteries to power everything. Running my arduino with one shield runs fine, but not with both shields stacked on top of my arduino. I've even tried powering it with an extra 4x AA batteries on my motor shield, but it still won't run. The way it's stacked is; arduino uno board, usb host shield then motor shield.
Its a very bad idea to power everything from the same battery source. Most motors, especially ESP, generate large current spikes, rather than draw a small current throught. AA batteries are not designed for this.
You can get away with using AA batteries for micro-controllers, shields. However, keep motors on a sweater power supply. There are batteries for specific motor types, and these will typically have a high current rating. Of course, without a circuit diagram, I cannot go into details. I'll update my answer when you do.