Thank you for your response.
A UMC hearing does not seem appropriate on a Motion to Strike Sham Pleading because as you describe the motion it necessarily involves substantive issues and contested facts. However, you may be able to obtain a Special Set Hearing by contacting the Judicial Assistant to schedule a hearing.
Note that Rule 1.190(e) specifically provides that "At any time in furtherance of justice, upon such terms as may be just, the court may permit any process, proceeding, pleading, or record to be amended or material supplemental matter to be set forth in an amended or supplemental pleading. At every stage of the action the court must disregard any error or defect in the proceedings which does not affect the substantial rights of the parties." Again, this means that the court will likely allow the amendment and supplementation of your ex's pleading. And under Rule 1.190 you have 10 days to respond to the amended pleading.
Therefore, you may want to file one Motion to Strike arguing both the violation of Rule 1.190 and in the alternative that the amended pleading should be stricken as a sham pleading and ask for a Special Set Hearing on that combined motion. One reason you don't want to wait to file the Motion to Strike based on the sham pleading is that, if that motion is denied, you still want the opportunity to specifically respond to the amended pleading and the court will likely give you the opportunity to file a response outside the 10 days if the motion to strike is denied. If you only file a Motion to Strike based on the Rule 1.190 violation then the court doesn't know there is a problem with the substance, will see there is no new opposition and may decide your ex's motion based on your original response. The combined Motion to Strike would provide notice to the court that there are procedural and substantive issues, and would likely preserve your opportunity to respond to the amended pleading should the motion be denied.
Generally, a response or opposition has some indication in the title
that it relates to the motion that was filed, and if you are filing for other relief in addition you add that to the title also. The court needs some way to match the motion and the response. If you mentioned the title of your ex's pleading in the response then the court will know that they go together. If you are unsure that your response will be seen as related to your ex's motion, you can call the clerk and let them know that the Motion to Quash and for Protective Order is also a response to your ex's motion. You can also send a notice of clarification to the court.