Lucrecia wanted to stay with Hojo? I was always under the impression that Hojo abused Lucrecia and impregnated her against her will. I also doubt that it was with her permission that he injected JENOVA cells into her. I always felt that Vincent was pissed because Hojo violated Lucrecia and wanted to get revenge, then was shot and experimented on. I just cant imagine that Lucrecia would want to be with a psychopath like Hojo.
Oh and in case you wonder about Aeriths parents: They were Professor Gast and Infalna. Hojo later had Gast killed and kidnapped and experimented on Infalna, but she escaped and died at the train station shortly after asking Elmyra Gainsborough to take Aerith. Which is how she ended up as Elmyras daughter.
I always wondered though: Is Aerith her birth name or the name given to her by Elmyra?