Hi Ajh824
welcome to the Apple (user-to-user) Community.
Re: iMessage-Android messaging : challenges communicating with my wife across messaging systems
Seems messages using the Messages app from Apple to Apple devices go by wi-fi, to and fro.
Yet on your wife's iPhone, using Messages for an SMS to your Android phone would require using cellular data.
If her iPhone's cellular data plan allows SMS MMS, it would need to be switched on for Messages.
She would also need your contact phone number listed in order to send SMS, (ie: not just your email address).
Apple support have articles online (links below) to help with details:
What is the difference between iMessage and SMS/MMS? - Apple Support
Use cellular data on your iPhone or iPad - Apple Support (NB Cellular data rates might apply.)
More info. if needed:
Messages Support Website (info / support / contact):
There is a "Get Support" link (at the very bottom), of their website (link below)
Messages for iPhone, iPad, Apple Watch, and Mac - Official Apple Support
All the best :-)