Before my second son was born I got a 60D and 18-135 and 50 1.8, and I'm very glad I did. If I were in your situation I would:
1. absolutely get a real flash that can be bounced. Natural lighting and wide apertures are great when possible, but especially after the kids are mobile a flash bounced off the ceiling is crucial
2. get a faster lens than 2.8 on crop - I think the shallow depth of field really makes a difference if you want your photos to look better than the average snapshot
3. go full frame - now is your chance! A 6D + 24-105 + 85 1.8 + 430 flash might be close to your budget if you sell your current zoom and shop wisely. If you had to leave something out maybe I'd leave out the 24-105 and add a 40 2.8 and then use a point and shoot for things where you needed other focal lengths. You're going to need a decent point and shoot anyways since you can't always lug the DSLR around, and if your DSLR can't autofocus in video (the 7D and 6D cannot) you'll probably want to just use your point and shoot for videos. I don't have much luck trying to focus manually with my kids moving around.
That said, if you're selling your current zoom, you're really not tied to Canon. I would consider some other brands, the nikon/sony/olympus 16mp+ sensors do noticeably better that the Canon for high iso and dynamic range. I've got lots of ISO 1600 shots that are too dark or too grainy to print big and put on the wall, so I have to stick with ISO 800 and flash a lot. Most other brands also autofocus during video, which is nice with kids. Yeah, this is a canon board and the canon sensor isn't that bad, but for the same money I think you can do a little better than canon right now.