There are instances of children being baptised twice. Most probably because, as far as the Church of England was concerned, the first baptism was not lawful, or "all things were not done, as they ought to be" Or the Parish Priest was deliberately kept in ignorance of the first one.
The first question asked at the Public Baptism of Infants in the Book of Common Prayer is "Hath this Child been already Baptized, or no?".Only if the answer is 'no' can the baptism continue. If the answer is 'yes' then the Priest has to examine them further as to the find out if the child was lawfully baptized, and if the Minister shall find by the answers of such as bring the Child that all things were done as they ought to be, then shall not he christen the Child again but shall receive him/her as one of the flock of true christian people.
Stan