Based on Zlatica's information, this is likely to be Ethel's birth:

https://familysearch.org/pal:/MM9.3.1/TH-1951-23096-43324-65...

No. 32
Dated in Nagy Rákos, May 21, 1897
Informant: Joseph Németh, farmer, residence Pankasz, known personally to registrar
Father: Joseph Németh, evangelical reformed, farmer, residence and birthplace Pankasz, age 38
Mother: Lidia Baján, evangelical reformed, farmer's housekeeper, residence and birthplace Pankasz, age 28
The birth: Pankasz, May 15, 1897, 10 a.m.
The child: girl, evangelical reformed, Etelka


And this may possibly be Carolina's birth:

https://familysearch.org/pal:/MM9.1.1/V53V-GFJ
Name: Károlina Baján
Event Type: Baptism
Event Date: 26 Oct 1890
Event Place: Nagyrákos, Vas, Hungary
Gender: Female
Father's Name:
Mother's Name: Lidia Baján
Reference ID: 213
Line Number: 44
Digital Folder Number: 004703499
Image Number: 00445
GS Film number: 630368

Did they have a sister named Vilma? "Nemes" could easily be a misreading of "Német"...
https://familysearch.org/pal:/MM9.1.1/V53V-LX3
Name: Vilma Nemes
Event Type: Baptism
Event Date: 12 Jul 1885
Event Place: Nagyrákos, Vas, Hungary
Gender: Female
Father's Name: József Nemes
Mother's Name: Lidia Baján
Reference ID: 87
Line Number: 34
Digital Folder Number: 004703499
Image Number: 00382
GS Film number: 630368

I've had no luck with Szidonia, however: the only one indexed by FamilySearch with a mother's name of Lidia Baján has the father's name indexed as István Gezgucs, and the only ones with a father indexed as Joseph Nemeth were born in the 1860s.

I think your best bet is to order microfilm number 630368 for viewing at your nearest Mormons.