Connection issues with servers in private and public hosting using the same domain name

I have a question about hosting addresses like AWS route 53 private, public.

I am using example.com as my public hosting.

I want to use a specific domain internally using vpn, so I added the same example.com domain as private hosting.

I want private.example.com to be accessed only from inside.

So I created two hosting domains.(one public, other private. Both have the same domain name.)

The problem is that one domain that was in the public cannot connect to the server.

public1.example.com is not connected, but public2.example.com and public3.example.com are connected well.

The problem is that only certain public1.example.com domains cannot be accessed. (Private domains can be accessed without any problems.)

In case, you set up private and public hosting on the same domain like this,

I wonder if it is possible to solve the problem of not being able to connect to a specific domain as above if I set a setting that I do not know.