Short answer: No mainstream game combines IMVU-style avatar chat with a dedicated pregnancy/baby-raising system. Here's why, and what comes closest.
| Game | Platform | Baby/Parenting Mechanics | Social Focus |
|---|---|---|---|
| IMVU (Roleplay) | PC, Mobile | None official. Players roleplay pregnancy/birth via chat & custom animations. | High (Avatar chat) |
| Avakin Life | Mobile, PC | No baby system. Marriage & pets only. | High (3D chat) |
| Second Life (Excluded per prompt) | PC | Full mesh pregnancy/baby systems via user-made attachments (e.g., "Mama Allpa," "Zooby"). Adult-only regions. | Highest (Sandbox) |
| Stardew Valley (Co-op) | PC, Console, Mobile | Marriage → Pregnancy event → Baby (toddler max). No aging further. Deep farming/life sim. | Co-op (1-4) |
| BitLife | Mobile | Text-based life sim. Detailed pregnancy, parenting, grandparenting. Single-player. | None |
| Tomodachi Life | 3DS | Miis marry, have babies (cutscene), raise to child. Quirky, not realistic. | Local/StreetPass |
If you want IMVU's aesthetic plus parenting, your best bet is Second Life (with Zooby/Mama Allpa) despite your exclusion, or a private Discord RP group.