Telling anyone directly that you don't want, or don't like their food is pretty much guaranteed to offend them on some level. Lying would be a bad idea too, because ultimately lies do get found out, and you said you have a good relationship with your neighbour which could be ruined if she even suspects you are lying.
The best kind of excuse would be a practical one - that is, a sound reason why you shouldn't accept food that doesn't involve your personal taste.
I presume that if neither you nor your family are eating her food, you must be eating your own food. Her food is getting wasted. But if you did eat her food, then the food you bought in for yourself would be wasted. This is the sort of reasoning you should use in response.
You could say something like:
I really appreciate the sentiment behind all these dishes you send us - it is very kind of you. But we do all our shopping in advance and when we get food from you we find our own food is going to waste. You really don't have to send anything over, we don't want any food to be wasted.
If she doesn't immediately accept this and still tries to insist on sending you food, just persist on the same line of reasoning. You aren't going to change your shopping habits because you are a family, and you save when you buy in bulk, so you can't just buy less food because it would cost you just as much or even more.
If you can't win with her, there is probably nothing more specific you can say without causing offence, so I would just let her give you the food and continue binning it. There is a possibility she just likes cooking and doing something nice for you. It might give her a bit of a purpose, and that might be worth the wasted food. But if she gives you a dish after you had the above conversation with her, just say something like:
Thank you. We do have a meal planned already for tonight, but if we have any room we will give it a taste.
You could perhaps try returning the dish to her later on and say something like:
We were so full after our meal we didn't get to try any of this. Would you like it back for yourself?
Or, if that isn't possible, and she later asks you if you enjoyed the dish you could say something like:
I'm really sorry, we were so full after our meal we didn't get to try any.
One final thought about the wasted food - have you checked to see if there are any homeless charities nearby that would appreciate the food? You could donate it to them and then at least you wouldn't feel guilty about the food not being eaten! You could also tell her quite truthfully that the food was appreciated and enjoyed.