The TX Court through which the Plea in Intervention was issued and served has its own unique statutes and Rules which govern the pleading process and trial practice. In general, however, "intervening" or "interpleading" is related to adding a new or third party to a claim after the original Complaint has been filed and served in a Court action. Apparently, your sister-in-law must have some interest in or control over her late Mother's property or assets from which Dallas County wants payment of the pending tax bill to be made.
The specific and detailed answers to these questions, which will be determined by the TX statutes and Rules which govern the pleading process and trial practice in the Court which issued the Plea in Intervention, can only be obtained via your sister-in-law's personal consultation with an attorney licensed to practice in TX who knows the applicable TX statutes and Rules which are above described for you. Your sister-in-law should be prepared to take with her all of the papers related to the Plea in Intervention that were issued to her by the Court, together with all documentation related to her interest in or control over her late Mother's property or assets.
Your sister-in-law should also be prepared to pay a fee for the attorney's consultation, review and advice. The amount of that fee, and the terms for the payment of same, should be agreed upon between your sister-in-law and her attorney before they begin the consultation.
An Intervention is some third party joining their claim to an existing case. Perhaps your sister-in-law is making a claim, and the County wants to collect their money out of what she receives? If she owns the house (as her mother's heir) she will owe the property taxes.