I have stayed at the DLH 7 times in the past five years and have a reservation to stay there in October. So I clearly like it very much! I have also stayed at the GCH and the Paradise Pier as well as quite a few places at WDW. GCH is more of a wow factor with the lobby and the rooms have some very nice features the DLH rooms don't (turn down service, nicer linens and toiletries and a balcony). However, I didn't like the pool as much, our room was much smaller and darker and my kids even at 12 and 14 prefer the DLH. I love the grounds, the light, bright room that are spacious and the fact that with each room at the DLH you will either get a daybed or a rollaway. The GCH simply doesn't work for me, my 14 year old son is too tall for the bunk beds and its not acceptable to me that my extra bed might very well be a sleeping bag! Given the age of your kids, I would definitely give the DLH a try. I don't find the rooms as luxurious as the Grand's rooms but we have never had a dirty room (always spotless) in all our stays there. And I find the rooms to still be very nice (maybe on par with a Marriott or Hilton but with those Disney touches and theming). My brother and his wife also prefer the DLH, they have twin girls who are 8 and even though they always stay at very nice places (five star) they prefer the DLH for the room size, theming and atmosphere as well. Their girls miss the Neverland Pool when they stay at the GCH!
And a premium view at the DLH is very nice, you will either have a lovely view of the Neverland Pool or DTD and DL. If you get that one, you will have a wonderful view of the fireworks. The rooms don't have balconies, the only detriment to them in my opinon however they do have sliding doors to allow in fresh air. Again, the DLH isn't as deluxe as the GCH, it wasn't built by Disney so it doesn't have that immersed in theming sort of feel. However, I love the Disney touches throughout the hotel, it has great dining options and lovely grounds. It also has two pools, an arcade and these very cute little jungle cruise remote control boats and lovley koi ponds and waterfalls. So there are lots of things to do and explore around the resort that are very kid friendly.
I stay on points at DLR and find the premium view rooms at the DLH a good deal. I also don't find the walk to
Disneyland that much longer from the DLH. Both times we have been at the GCH we have been down long, confusing hallways and the trek down them plus through the lobbies isn't that big of a sell to me. The hotel itself is closer, but your room may not be that much more so. A premium view room at the DLH will put you in one of the two closer towers to DTD and the parks. The walk from the DLH to the parks is around 10 minutes. And at night, following the fireworks, you can easily get on the monorail. From DL, I find the DLH much easier to get back to. From DCA, obviously the GCH is.
You can't make a bad choice but I say give the DLH a try.