I'll try to give some specific examples, as this one is rather difficult to explain.
Example 1: Imagine you have been attending a kindergarten in Canada. Now you are 30 years old, so you won't go to kindergarten again, but I want to ask you whether you would be happier today, if you were attending a US kindergarten in the past. Would it be like this?
Would you like to have been attending a US kindergarten?
Example 2: You have been brought up by a stepfather. Now you are an adult, so nobody is, nor will be bringing you up anymore. But yet, I want to ask, whether you would be happier, if it were your real father who brought you up. Would it be like this?
Would you like to have been brought up by your real father?
Alternatives, or how are they different?
Would you have wanted to attend a US kindergarten?
Would you have wanted to be attending a US kindergarten?
Would you have wanted to be brought up by your real father?