school registration

(Oregon) My husband and his ex just finished mediation for custody of their son. The agreement was Joint Legal Custody, Shared Physical Custody. Their son is 3 1/2 years old and can start pre-school this coming year. We have our son from Friday morning until Tuesday night and she has him the rest of the week. She isn't registering their son for pre-school. She has the papers and everything but she's too lazy to fill them out. With the way the custody is, us having him the majority of the time, can we take over all that kind of stuff. Their little boy has lived with her since birth. This is the first time he has legally lived with us. Are we overstepping everything taking over what needs to be done? Because he lives in 2 different houses during the week do we have me have her sign papers as well to get him registered? Registration started in March and she still hasn't turned them in. I've offered to help her fill them out and she always has an excuse. Thank you for your reply.