Mina,
with the seats up front and on the back the bike will be quite hard to handle.
I did that but only occasionally, for a very short distance with the smallest kid in the front basket:
How big are your kids and how much do you weight?
How long do you want to run with this setup? With two 30lbs kids up there, especially if they are not mellow, it might be quite a challenge - I have not spilled my kids but I had white knuckles moments with "jumpy" cargo.
Another possibility would be to have one seat in the back (or front, but back seat will last longer) and a child carrier like Ergo (it actually quite comfortable, at least with my hybrid bike).
I don't have Ergo pics on the bike, but this is Ergo:
But I agree with previous posters, that trailer would be best - I used to chain the trailer at the daycare parking lot so I did not need to drag it with me.
While Burley or Chariot makes nice trailers, don't discount cheap InStep/Schwinn - we put 3 seasons of commute in an el-cheapo trailer and while the fabric was stretched, we still sold it on Craigslist with some life left.
Bakfiets are excellent (especially in colder climate), but I could not afford one.
If you insist on front+back seat, I would probably put Bobike mini in front and any decent seat in the back (Bobike Maxi is nice, but there are much cheaper back seat options available used on Craigslist)