Family Sharing & Itunes

I just had a ridiculously frustrating conversation with an Apple Rep and as such am seeking guidance from the community.

My wife and I have an iMac, an iPad and each have an iPhone X. The imac, under my login, has a rather large collection of music that I've purchased and ripped from CDs or bought and downloaded from various services.

I can access the music via my iphone and ipad from anywhere in the world and have iTunes Match enabled and share my itunes via iCloud. I also created and enabled family sharing which I assumed would allow my wife to access the music from her iPhone. That doesn't seem to be the case.

The rep from apple insisted I had to pay for the streaming service which infuriated me... why should I have to pay to share with my family what I already paid for? Finally her work around was to have me login as myself on my wife's iPhone's iTunes to access the music.

This seems like a terrible way of doing it. Does family sharing solve this problem? Is there a better way of sharing music from itunes with my family members?

Any help would be much appreciated.

Thanks