I had a recent club-level stay, with an almost-four-year old boy, and wasn't impressed at all (we'd NEVER go back), but if you have your heart set and think you'll love it I won't try to talk you out of the Polynesian.
In terms of snacks, you're just as good stopping at a grocery store and spending $150-$200 on breakfast stuff and drinks and maybe a box of goldfish crackers as you are with club level. It will save you a bundle and probably give you a better selection.
What we liked about club level wasn't the food, which was scarce and not replenished, though I did drink quite a few diet Cokes and my husband had, I think, four beers in our week-long stay. (Son and hubby also had cereal and fruit, or yogurt, for breakfast each morning we didn't do a character breakfast.) Instead, it was the community.
The rooms at the Polynesian are not huge, though they are often described so on this forum. There's nothing wrong with the size, it's just very standard hotel room size and that can feel a little close with a little one, especially when you consider that they will spend their entire day at Disney under strict control: waiting in line, holding your hand, in a stroller, etc. Also, as an only child, my son got a little lonely for other kids to actually play with during our week stay.
In the lounge, my son loved the kids' area (some smaller furniture and a TV set) and, more importantly, the kids he met there. He actually liked that as much as the parks some days and had a great time with various little ones throughout our stay.
Husband and I enjoyed having someplace besides the room to sit, and we chatted with quite a few other guests there and met some very, very nice folks. We also watched the fireworks from the lounge twice during our stay and that was nice too, though if it had been warmer we'd have preferred to watch from the beach.
Was it worth it? To my mind, no. But only you can decide if the cost-benefit works out for you and your family. I do know that as an "only" my son often asked to go to the lounge, in lieu of just back to the room, after a day out in the World.
EDITED TO NOTE: When we went it was really cold, so meeting other kids and playing by the beach or pool wasn't an option. If it had been, the lounge would have been even less valuable to us. In the end, we decided our next visit will likely be off-site. We toured the Hilton at Bonnet Creek and the pool area exceeds anything we saw at Disney, even Yacht and Beach (in my opinion), and the standard room we saw was bigger than the Polynesian, or at least looked that way because it was brighter and newer. And, frankly, for the cost of a night at the Poly you can get a suite at the Hilton (or even the Waldorf) both of which exceed anything I've seen Disney offer. And driving there was no farther than Disney hotels, to be honest, assuming you've got a car (and the rental cost would still make the Hilton cheaper). The only thing we'd miss is the great Polynesian ferry to the Magic Kingdom. If you stay in the Hawaii (club level) building it's practically right outside your door and can have you at the gates in under 10 minutes. Very nice.
