If he was legally adopted then no need for other parents ok. You're legally the parent. It shouldnt be an issue to begin with since have same name. Just have him call you mom and there should be no issues. If you want bring the adoption court order.
As for the other children. Dp you have sole custody or joint? If joint then technically you need their permission. Sole you dont. Again if they just call him dad and you mom, there should be np issues.
Note this is only for entry into ITALY. Other countries can have other requiremrnts to enter, rven within Schengen area.