Hi Josie
I'm not surprised you're frustrated - the father is usually named even if he is dead, but you can guarantee he won't be named if it's really important to find out!
I've got one in my tree like that and I'm not doing at all well finding him

I think your best bet is to find Amelia's baptism record and really hope that the family was Church of England

According to the Somerset record office, they have the registers for Butleigh. I haven't been able to find any record of them on-line, and they aren't in the BVRI either but perhaps someone else in Rootschat has access to the Parish records. It's probably worth posting another request for Amelia's baptism on this site. At some point I'm going to have to go to Somerset Record Office myself, but it won't be until next month at the earliest.
Sorry I can't help more but there are some other very knowledgable people on the site who may do better

Good luck
Angela