There's nothing morally wrong about either reselling or haggling for charity shop finds.
Haggling comes down to a simple exchange. You'll only pay what you find acceptable, and charities sell for what they find acceptable.
If you wouldn't pay the 'sticker price' then it's reasonable to give the shop your best offer. If it's OK with them then it's a win-win.
If the shop isn't willing to let the item go for the price that you find acceptable then the sale won't go through. Again, no-one is losing out.
Offering a lower price isn't 'ripping off' the shop. It's giving it the chance to sell you an item that you might not otherwise buy.
If you choose to pay more for an item than you might otherwise then you're effectively giving a donation. That's fine, too.
If the shop has a 'no haggling' policy then that's also fine. They aren't compelled to give you a discount.
You have a moral duty to do the best for you and your family. Charity shops - even if you haggle - will benefit if you buy from them, so why the shame or guilt?