No. You do not need this form as long as he claims your eldest son and you claim the youngest.

Form 8332 is for when the custodial parent ( one whom the child spend more than 6 months during the year) releases the right to let the other parent ( noncustodial parent) to claim the child .  In that case, the noncustodial parents will be entitled to the exemption / dependency and the child tax credit and the custodial parent is granted the Earned Income Credit, Head of household and the Child Dependent Credit.

Please see attached.

https://ttlc.intuit.com/replies/3301985