She has 3 beautiful children from her marriage
Where are the kids and did they get there legally?
Is the only option we have, to wait until they come of age so they can apply themselves?
No, you can petition the family court to issue passports without his signature being needed. The process is basically that you send a letter to him via registered post asking him to sign the enclosed applications for passports and to have his signatures witnessed by a notary (you should offer to pay for that, ask him to say which notary he wants to use and that you will then pay in advance the fees for witnessing his signature). Then you wait three weeks (two weeks for him to get the registered letter and one week for his reply to get to you), then you send the same letter again and wait another three weeks. After that you can apply to the court for them to waive the need for his signature.
However, doing that might stir him up and make him realise that by stopping the kids from getting passports, he can make life uncomfortable / inconvenient for the mother.
he exists just to cause as much hurt and trouble for his ex wife as he possibly can.
Unfortunately the Polish family court will give him ample opportunity to do that.