Ask Mr. Smarty Plants

Thank you for clarifying your information and giving Mr. Smarty Plants an opportunity to amend the reply. You are correct that the USDA identifies as allelopathic a cultivar of Artemesia ludoviciana called Summit. A comprehensive search of national and international research literature did not yield data to corroborate this information. Only a DNA analysis will identify the correct cutivar of your Artemesia. Mr. Smarty Plants guesses that this would not be an easy or attractive option to you. Chances are the artemesia is not toxic to a well-established plant, but you may be unwilling to take that chance with your two lovely native trees. If that is so, Mr. Smarty Plants suggests removing the Artemisia and planting a different ground cover between your trees. (You could move that Artemisia near something you want to get rid of and see if the Artemisia will do the job for you!)

The point here is that when you are dealing with cultivars and hybrids, you seldom know what the parents of the hybrid are or what their characteristics were. It's unlikely that the vendor who sold you the plant knows, and probably not even the wholesaler who grew the plant in greenhouses and shipped it to your local nursery. Although allelopathy can work through roots, stems or branches, it is most often exhibited in trees shedding their toxins on plants having the audacity to try to grow beneath them. It might kill freshly emerging seedlings, but you probably aren't trying to establish a viburnum forest anyway. 

So, your next question might be, what should replace the Artemesia? Appreciating your commitment to Texas native plants, return to the Native Plant Database. Select location (Texas), habit (grass or herb) and duration (perennial). The requirements for your site will probably be shade and dry for light and soil moisture. Using that information, Mr. Smarty Plants found 9 grasses and 43 herbaceous plants potentially suitable for your site. Good luck!