The notice of appearance is to reactivate the attorney's participation in the case so papers can be filed electronically and so your ex is officially on notice that you have an attorney. Whatever designations you had in the original case remain the same no matter who is bringing the motion. So if you were the Defendant in the beginning, you will remain the Defendant. More importantly, these are questions you should be asking your attorney, who is in the best position to know what is going on with your case.
Responses are for general information purposes only, and are based on the extremely limited facts given. A consultation with an attorney experienced in the area of law(s) indicated in the question is highly recommended. Information and advice given here should not be relied upon for any final action or decision, as the information is limited by its nature to the question asked and the fact(s) presented in that question. THIS RESPONSE DOES NOT CREATE AN ATTORNEY/CLIENT RELATIONSHIP, particularly considering that the names of the parties are unknown.
A Notice of Appearance is simply notice to everyone involved in the case that the attorney is the "attorney of record" for the respective party in the case and as a result, will serve as contact for the client and should be served with all documents in the case. The original party designation in the complaint or Decree will continue throughout all subsequent motions in the case.
I agree with the Notice of Appearance answers - so I won't expand on that. But, generally, you will both be considered "Joint Petitioners" and the original caption should remain. However, often a moving party will re-caption the matter in subsequent motion practice - which is technically improper. You should caption the matter property, mirroring the original papers, but make a note in your responses/follow up pleadings (in a footnote or someplace) that the caption is wrong and needs to be clarified to be accurate. If the "Ex" calls him/herself the plaintiff incorrectly, it could confuse the court and they could be led to believe she should have opportunities to "reply" that don't actually exists. Just make sure you clarify this, or, reach out to the counsel and ask to clarify this for future pleadings.