In answer to your many question's, her original husbands first name was Horatio, bu it is alleged that she moved to the Chicago area without him. As for immigration records, I haven't looked because I wouldn't know where to begin ! We aren't even sure if she kept her maiden name or used her married name or took on the name of another. I checked the IL online database for deaths and Golden/Goldie Smith and your right there appears to be no Golden Smith or Forshner/Foshner deceased in the period around 1934....

SMITH GOLDA F/N UNK 2480262 1924-10-13 KNOX GALESBURG 24-10-14
SMITH GOLDA MILDRED F/W UNK 0021999 1916-05-19 LOGAN LINCOLN 16-05-22
SMITH GOLDEN ESTELLE F/W Y-59 6031610 1949-11-04 COOK 49-11-04
SMITH GOLDIE F/W UNK 0550200 1925-07-22 MCDONOUGH INDUSTRY TWP 25-07-23
SMITH GOLDIE F/W UNK 0021218 1946-05-30 SANGAMON SPRINGFIELD - -
SMITH GOLDIE F/W UNK 0026818 1948-07-04 CLARK CASEY TWP - -
SMITH GOLDIE A F/W Y-57 0000864 1942-01-09 COOK CHICAGO - -
SMITH GOLDIE AUGUSTA F/W UNK 0016939 1918-04-02 FULTON BERNADOTTE TWP 18-04-04
SMITH GOLDIE MAE F/W UNK 2720811 1932-09-02 PEORIA PEORIA 32-09-02
SMITH GOLDIE MARIE F/W UNK 0280324 1929-06-11 FRANKLIN BROWNING TWP 29-06-15

She is almost certainly buried in the US.... The information I have states that the family received a letter stating that she had been murdered and some of her things had been returned to the them.... NO indication of any children....

Many thanks