Could it be this? The john lewis mother marches to the beat of her own drum. Has no inking of usual party dos and don'ts or is she has, doesn't really care. And in some ways, I applaud her for this.
She is not being partiuclary materialistic - in fact the 'expensive' present she has in mind might be one costing all of £10.00. And she is expecting people to give £1.00 or £2.00 each, no more. In fact, this is her way of saying, "look I don't want you to give a present, as I know there are three birthday children and giving presents to all can get really expensive, and leaving out two host children to give to one can seem a bit mean, and well it's all just such a minefield ..."
The last time I looked at a John Lewis toy department, there were lots of pocket money toys, small lego sets, beyblades etc.
She wants to share in this three way party, but feels it is an organisational nightmare when it comes to sharing out presents and guests buying presents. And she would be right about that, no denying it.
So, she has done some lateral thinking and decided to give guests the option of giving money for one big toy, making it (in her opinion) a neater and easier way to give a gift. And it's also a stand against getting needless junk. After all, it is the norm that a guest would bring some gift to a party, however much the host protests.
And perhaps her child, far from relishing the idea of unwrapping surprise gifts, has their heart set on this special toy at John Lewis. Perhaps the mother talked it over, and her child is really keen on this other idea.
And last year, perhaps this same child was not happy (for some reason) with the gift sharing arrangment that took place after the 3 way party. Perhaps the child felt the other two got better gifts than they did, however fair the adults thought the present giving was.
OK a lot of perhapses. My sympathy with the John Lewis mother would instantly go if she had produced an actual present list (very materialistic, that) or has in mind a really expensive toy - and tells people what it is. But AFAIK I don't think she has done either of these things - she wants contributions to a single mystery present which might not be as expensive as people assume.
I hope guests can contribute money anonymously - a bit tacky if it's public knowledge how much each parent put in the pot.
I don't like the idea of present lists for children's parties, but can see there could be mitigating reasons if there are three hosts.
Come back OP tell more! Your story IMO is open to different interpretations.