I have no experience with these programs, but as people are saying it would be fine, you might want to ask whether i7 is worth it, maybe i5 will do....
If you are this concerned with editing, I would go ahead and get the MPB 15" .. The MBA is designed to be a light portable machine that can handle basic tasks. Just so happens that the technology has moved past "basic" at this point. However in another year you will be in the same boat of the MBA slowing down as the applications develop to take advantage of the hardware.
Just my .02 cents but if you're buying the MBA, buy it for it's portability not its power.
web development and graphic works for website development don't need high dpi images to work in pixelmator. so the machine will be able to easily eat those tasks.
family video editing might take a little longer than the mbp 2011 lineup, but hey, it still does the job, only a bit longer.