Thanks for your post and the very interesting question.
Since you will be travelling with German documents (Personalausweis and/or Reisepass), you can cross the border to Northern Ireland without the requirement for a visa, correct. You can read more about visa regulations here
For your wife the rules will be different and I would recommend getting in touch with the Irish
embassy directly to confirm the exact requirements in her particular case.
Please keep us posted on how you get on and feel free to let us know if you have any additional questions or need more help with your travel planning.