Remove iCloud

Before disbanding the family sharing account ( you as the organiser ) see the article Remove family members from a Family Sharing group on Mac - Apple Support

Children under 13 can’t be removed from a family group (age varies by country or region). However, you can move a child to another group using Family Sharing.

Now you can disband the group see the section - Stop Family Sharing

in the article Change Family Sharing settings - Apple Support

The account is now non family sharing account and every member is removed .

If your wife is using a different Mac / iPhone and her Apple ID is signed she can create a family sharing account ( and will be the organiser onwards ) , she has to invite you and you have to subscribe the invitation to get joined in the group Set up Family Sharing - Apple Support

The child is seven years see the section - Change the date of birth for a child

In the article Update the date of birth associated with your Apple ID – Apple Support

( a ) you had a different family sharing account ( you as the organiser ) .

( b ) your wife has different family sharing account ( she is the organiser ) .

In both account the son is member of their group .

I tried sending an invitation from my wife to my son’s account, - no you can't send invitation , your wife can sent the invitation to son ( but before that son has to leave your family sharing account ) .

Note : there are two family sharing account say two Mac or whatever device is used , the two apple id and password with account credentials should be always different in individual device Mac / iPhone whatever is used .

Regarding , Apple Watch that is connected it can be removed from the account Change the Trusted Device list for your Apple ID on Mac - Apple Support

In the article Create an Apple ID for your child - Apple Support - see the section About settings and features for kids under 13

See Make sure that each family member has a unique Apple ID - Apple Support

Also you mentioned - but my phone did not receive the request to transfer him.

Because your wife transferred the son to another family sharing account , you didn't transferred the son to another account , that's the reason your iPhone did not received the request .