All the suggestions above, I have done (for the record, my wife is the Family Organizer), but no matter if I or she initiates a new home, the other family members are listed automatically as available and we can invite them.
Here's the problem - I can see this happen in real time - if either of us invites the other from a new fresh Home, immediately after inviting the other, the "inviter" goes from being the "Resident (owner)" to just "Resident" and then the invitee never completes the joining - it just spins and never joins. Even if I cancel the join, the original Owner is just a Resident - no one is the Owner anymore.
So, here's the weird thing: I had my daughter's iPhone start a new home and invite the two of us. She does not get the Resident/Owner error and we can both join. OK, but once the second of us joins, it seems to merge the two of us into one "person". Our phones only show our daughter as the Owner and then ourselves - not the other parent - in fact it has merged my wife and I as a single user under the Home. We can use the Home somewhat normally.
In my wife's detail view - in small grey text under her name - it says: "iCloud: her-email@mac.com" and then "Media: my-email@mac.com". Although my daughter has made both of us Admins, we are not allowed to add Accessories. And Recognize my Voice seems weird - I cannot make personal requests...
Here is where the issue may be: I am the main iCloud account, but my wife is the family organizer. This seems to be where it is screwing up, maybe??