We have given my daughters caste as roman Catholic during her admission in a ICSE school for LKG and UKG, which is the mother's caste. Can it be changed to SC in 1st standard, during readmission in the same school, which is the fathers caste Or do we need to change her school to submit a change in caste ?

There are many factors at play here.

1. The validity of Caste certificate differs from State to State. For example, in Karnataka, Caste Certificate has lifetime validity, whereas in Kerala it is 3 years. As most of the states in India provides caste certificate valid for atleast 3 years, it will be difficult to get a new caste certificate. (Details about State was not mentioned in the question)

2. To decide the status of an child of a couple where one of the spouses is a member of SC/ST, the crucial test followed is to determine whether the child has been accepted by the Scheduled Caste community as a member of their community and has been brought up in that surrounding and in that community or not. If the child has been accepted by the Scheduled Caste Community and has been brought up in the surrounding of Scheduled Caste spouse then, the child would be treated as Scheduled Caste.

3. If both of the above conditions are met, it also depends on policy of School whether to accept the child with change in caste or not.

You can apply for a new caste certificate by providing proof of caste as Father's Caste Certificate.

If you belong to any of the State, click on the below links to check the process to  apply for caste certificate.

Caste Certificate in Kerala

Caste Certificate in Maharashtra

Caste Certificate in Andhra Pradesh