Findmypast has the original parish records for Anglesey Churches, and you won't be surprised to learn that there are comparative few Thompson records - for instance only 72 baptisms.

It is well worth exploring those records to see if they can unblock any barriers.

The 1853 baptism for Catherine is in Llaneilian Church which is the next parish to Amlwch and its very common for the 2 places to appear in the same families.