Alright, a couple things here...
First, the cage. The size is fine - larger is always better, but it does meet the minimum size requirements in the US (other countries have different standards). The hedgehog's safety is the first concern when deciding on a cage - if you have other animals, then you definitely want the cage to be safe. A C&C is NOT an appropriate choice if you're looking for an animal-proof enclosure. Please do not use one for your hedgehog, especially with the pig in the house. They're not sturdy enough to stand up to a determined pig or dog wanting to get inside.
In my opinion, the pack'n'play would be difficult to use for a cage. I've had to reach into those before and it's a pain. Granted, I'm short & have short arms...still a pain. I wouldn't want to reach into one multiple times a day to try & lift out food/water dishes, a hedgehog, etc. I would really suggest sticking with the storage tote cage, and make sure the top is completely secure. The only alternative I would suggest, especially with the pig in the house, is a Critter or Ferret Nation cage, which are very sturdy & safe. They're expensive, but they're well worth it.
Also, they do make Christmas tree tubs in clear, and I've seen a few reptile people getting them recently on Tumblr. I know LarryT used them for cages as well, not sure if he still does. Check at home improvement stores like Home Depot, they may carry them.
Back to the playpen thing, if you're only planning to use it to keep your hedgehog in while cleaning the main enclosure, I wouldn't use a playpen at all, especially if the other animals are still a concern. Most playpens I can think of wouldn't be particularly sturdy against the other animals. You need a hard-sided cat/dog carrier in order to travel with your hedgehog anyway, so I would just use that to put them in while you're cleaning the enclosure.