does she belong to this family?
When you ask, "Does she belong to this family?" We are assuming you mean as a child to her parents?
A 1930 United States Census would help prove that she does, but that record does not seem to be available.
We looked at the Timeline in her Father and her Mother's Family Tree records. Her father's timeline shows that he registered for the Draft in 1917 in Escambia County, Florida, United States. So that possibly puts the family in Florida five years before Kathleen was born. Her mother's Timeline shows the death of her father (Kathleen's grandfather) in 1922 (Kathleen's birth year) in Escambia, Florida, United States. That again suggests the family had ties to the state of Florida, even the county where Kathleen was born.
That is enough circumstantial evidence to suggest that she is a child of this family. Hopefully more records will become available in the future.
As you can tell, the Timeline in Family Tree can be very useful for tracking the movements of your family. Here is an article from the Help Center about Timelines.
thank you so much for the information so well your time, kindly.