I don't have a pet, so have never been in there, but have been (in that shopping center) to Chevy's, TJMaxx, PayLess, AutoZone, Home Depot, Staples, Michaels, Bed Bath & Beyond, Capitol Discount Merchandise, Noodles & Company, Coldstone Creamery, Radio Shack, 5 Below, Shoppers, IHOP, Starbucks (of course) with no issues.
I was asked to leave Target in Springfield Mall, but didn't mention it because it's not "near Belvoir" in my book <grin>. (There's a post on that in the OC in NoVA thread somewhere here around page 119). I was escorted from the Mall by no fewer than four UNARMED individuals, and since then shop at the Target on Rte 1, where I have no issues. I haven't found anything at Springfield Mall I can't get elsewhere.