There are things we can not explain but I ask Allah that he will replace with a healthy baby in future Insha'Allah.
If the baby that has passed away was 4 months or more then this case the child's soul had entered in his body and therefore is treated as the same of a person who's alive and then dies and that is washing the body and then praying over it then to bury it with the rest of the Muslims.
therefore, if your baby was 4 months and older then that is what you should have done and if you have done that then you should have buried it with the rest of the Muslims where they are buried and you should not have buried it in your back yard or where you live or your mum lives too, this is what Islam teaches us and we must follow and take our guide from it. And I would advise you to go to your local Masjid and speak to the scholars there and tell them what has happened and they will inform you what to do next because the baby should not have been buried where your mum lives or anyone's back yard. Allah knows best.