automatic power source selection
from your written descrioption, here;s what to do.

find a relay that operates from 18V (most relays marked 24V will work just fine, or ones marked 12V with a resistor half the coil resistance in series) you'll need a relay with two change-over contats "DPDT" or two relays with single change over contacts.

what you do is use wire the relay coil(s) parallel  to the power input to the 10W amplifier, and put a switch before that so you can cut power to the 10W amplifier and the relays.

in the output from the Li-Po put the contacts of the first relay that are 'on' whern the power is off. 

in the input to the speaker use the other set of relay contacts to select which amplifier to connect the speaker to..

with the 18V present and the switch on the relay turn off the 1W amplifier and connects the speaker to the 10w amplifier, if you turn off the switch the 10W amplifier and the relay are unpoweed, the onpiwered relay selects the 1W for the speaker and connects the 1W amplifier to the ip-po battery.

the buck converter that charges the lipo is connected to the 18V input so it's on anytime the power is connected.

you'll probably want to add a switch that turns off the 1W amplifier and possibly also the 10W amplifier too. (switching both with one switch requires a dual pole switch)