Hi Seraphine, I was in exactly the same position as you last year, albeit with a DS, not a DC. My son chose with his heart (WGSB), we naturally supported him and it was the best decision we made. He's only a few weeks in, he loves it and I truly believe it's the right school for him. Not sure where this "snobbery" (please forum members don't shout at me for using this word!!!) comes from, but it is there, possibly like Pettswoodfiona said, because it's nearest grammar rival is a Superselective, which on visiting, my son felt that he was "very different" (his words not mine!!) from the boys that went there. Bexley doesn't have superselectives the schools are looked at in the same regard, it just comes down to preference. If the Wilmington schools were 2 miles over in Bexley, I'm sure they would be looked at the same as the Bexley schools. If it makes you feel slightly more reassured, 8 (I think) girls in my DS's year chose Wilmington girls last year, despite having a pass in both boroughs - it was the most popular girl's choice at this primary out of all the Bexley and Kent grammars.
Good luck in making your decision, I'm sure you'll make the right one and your dd with thrive.