I don't see the Uno as any more appropriate for "driving and powering" than the Esplora.
You can access some on-board regulators on the Uno that the Esplora lacks, but they provision modest demand.
"Linkage"? There are I/O pins on the LCD headers that can be used like I/O on the Uno (but not with the LCD in place). I haven't tried it yet, but the SoftwareSerial library may work with the Esplora, too.
The Esplora may be capable of the entire project.
A Follow-up (despite no Reply from OP, gotta love it)
Softwareserial IS Esplora compatible.
A serial resistor between the Esplora TX pin and the 'Uno" RX pin keeps the Esplora from "ghost powering" the 'Uno' when the latter is not 'On'. (I used a 20k, 10k-22k should do.)
The Esplora buttons could do with some debouncing / lock-out (in software).