When I think "estate sale" I think breakables, antiques, etc.
No way would I attempt to sell those on ebay! Too much can go wrong - damage, complaints, mistakenly selling a knockoff/reproduction.
It takes only a small investment and then a few months of waiting time to start, but since you have kiddos, this is what I have done to dress my kids for free, which I guess is the same as bringing in a small income!
(You could definitely put more effort into shopping for great deals and buying with the purpose to re-sell.)
I don't particularly like Gymboree or Mini Boden (I personally think Target clothes are cuter!) but some moms lose their sense of reason when it comes to those brands, and that's where this pays off: Buy your kids' clothes either new or in very good condition from ebay - only buy the brands that resell at a high price, and that most moms have heard of. Gap is another good one. Don't buy anything Gymboree or Gap *outlet* though, people turn their noses up at that for some reason.
This goes for shoes too - it helps to figure out your kids' European shoe size and search by that for the higher end kids' shoes.
So your kids wear cutie pie clothes, you are careful to get stains out [but don't worry if they ruin their clothes, people will buy ANYTHING if it's the right brand, and as long as you're honest about the condition, you're good!] and then you pack the clothes away once they've outgrown them.
And you wait...until you notice that Target/Kohl's/wherever you shop is starting to put the next season of clothing out. That's the time you list all of next season's clothes.
You make more than you paid (because you got such great deals of course!) and you put some away and use some to buy your kids' next round of clothes....
Until they're 10 and they insist on buying clothes from Target and then the party's over!
Anyway, you can do that with women's clothes too - I have an acquaintance who dresses herself gorgeously for free and makes a nice profit each month as well just by shopping at Marshall's, Nordstrom, etc. a couple times a week and knowing her brands.