Gerald married toms fathers sister
toms brother married Geralds daughter
tom married geralds brothers daughter
I believe you have the first relationship wrong.
The question makes the 1st statement:
Gerald is Tom's father's brother-in-law.
There are two kinds of brother-in-law; my brother-in-law can be either (a) my wife's brother, or (b) my sister's husband.
So Gerald, being Tom's father's brother-in-law, can be either (a) Tom's mother's brother, or (b) Tom's aunt's husband (= Tom's father's sister's husband).
In your answer, you go with (b) that Gerald = Tom's aunt's husband, and not Tom's wife's sister.
Now, the 3rd statement is:
Gerald is Tom's father-in-law's brother.
There is only one kind of father-in-law = your spouse's father.
So, Tom's father-in-law = Tom's wife's father.
So, Gerald is Tom's wife's father's brother.
Or, stating the same thing the other way round: Tom is Gerald's brother's daughter's husband.
So, since Gerald is Tom's father's sister's husband, that puts Gerald and Gerald's brother's daughter in an incestuous relationship.
The 3 statements only work (morally) if you go with the other kind of brother-in-law.
Now, the 3 statements translate as:
- Tom's mother is Gerald's sister;
- Tom's brother married Gerald's daughter;
- Tom married Gerald's neice.
Supplementary point:
My neice is the daughter of my brother /sister. Question: can the daughter of my wife's brother be called
my neice, or is she my neice-in-law? Has anybody ever heard or seen (or used) the expression neice-in-law? (Same with nephew-in-law, uncle-in-law, etc.)