Did you want to go to the "mums parties"? What kind of event are we talking about - drinks parties in the evening in her home?
It sounds like you don't have much in common with her, so I am not sure you were missing much by not going.
Same with her WhatsApp chat group - if you don't enjoy the same kind of chat (she sounds a bit gossipy from the way you describe her, and you say you are not like that) then I don't think you are missing out by not being included.
I guess to me that wouldn't have an impact on whether I would do normal neighbourly stuff for people like taking in deliveries. My neighbours are personal friends in the sense we don't socialise together, but I am always happy to help them out and vice versa.
Sounds like she was hurt when you stopped taking her parcels, and that's why she stopped chatting to you when you saw her. I do kind of get that.
And given this, the fact that she asked you to take the food delivery implies, I guess, that she was genuinely pretty desperate? So I guess she and her son must be really poorly.
Anyway, taking in a large food delivery IS a fairly big ask, as if there was chilled and frozen stuff you would have to accommodate it in your fridge/freezer - I would struggle to fit it in mine, personally. So I think it's fine to say no if you couldn't do it.
I assume you let her know you wouldn't be able to, to give her the chance to find someone else to take it? Assuming you have her number.
If you have her number and DIDN'T text her to let her know, I think that would be quite spiteful.
Other than that, fair enough. But I would honestly stop stressing about the parties etc. Who wants to go to the parties of someone they don't get on with socially?
And if I were you I would take in her parcels, when it was convenient to do so. Because you never know when you may need help from a neighbour yourself. I've helped our, and been helped out by, neighbours in really tricky circumstances in the past (elderly relative needing rushed to hospital in a snowstorm and I had no childcare, is one example that stands out). That has really taught me the value of keeping neighbours inside, even if they aren't people I would choose to hang out with in my free time ordinarily!