A good place to look would be the regimental history: "Geschichte des k.u.k. Mährischen Dragoner Regimentes Albrecht Prinz von Preußen, Regent des Herzogtumes Braunschweig No. 6 : 1626-1701-1906" by Alphons von Wrede, Selbstverl. d. Regiments (= published by the regiment); Brünn: Rohrer; 1906. Sadly, this does not appear to be available on–line, but perhaps your local library can borrow it from somewhere else in the US? Or UK? Or maybe some fellow NS Forum friend knows how to find it electronically?
This includes lists of all officers at various points in the regiment's history and may include lists of awardees for medals and suchlike. It would certainly give you all of the regiment's actions and, though in German, it is printed in modern type (the not old style, thus easier for a modern English–speaker to decipher).

Another option would be the periodic KuK army "Schematismus." Many/most of these are available on–line (try the BSB: https://www.bsb-muenchen.de) and list all officers by regiment. Other NS Forum members will know other locations to find these. Unfortunately, these will not tell you much beyond listing your ancestor and his fellow officers along with their ranks and (oftentimes) their awards. For example: https://opacplus.bsb-muenchen.de/metaopac/search.do?methodToCall=volumeSearch&dbIdentifier=100&forward=success&catKey=6557063&isPeriodical=N. In 1813, for instance, Aylmer appears on p. 221 as a Second–Rittmeister.

If he was awarded the Maria Theresia medal, he would also likely appear in Hirtenfeld's Militär–Maria–Theresien–Orden book (also on–line via Google Books).

Hope that is helpful and, to quote one of our Forum Friends, "good hunting"!