Yes it would be rude.
If you don't want her contact, be polite, write back saying "no not necessary, thank you for your offer but we couldn't possibly take your money, the kids don't need more chocolate (haha) anyway" All very convivial. Just don't give your address and she can't send anything anyway.

But not answering at all would be rude, yes.

Not sure though why you care if she sends the kids presents? She is obviously happy to do so and it doesn't hurt you any to accept them and the kids therefore have that contact and will remember that they had it. Spoiling their relationship, albeit a superficial one, for your own prejudices seems really quite selfish. JMO though!