She's making too big a deal about everything. She (presumably) heard you all discussing the fact that the get together was going to be pot luck, even if she didn't hear the part about who would actually bring what. You gave her an out by saying as it was her first time she didn't need to bring anything, so how was that tricking her? More than likely if you hadn't mentioned anything about potluck at all she'd have turned up and taken offence at the fact that you
hadn't told her. Either way you couldn't win.
She feels "trapped" into coming?

Good grief. It's a simple pot luck meal - it's not a summons to eat with the Queen of England. If she doesn't want to come she can simply say she has something else on. The day/meal won't fall apart if she's not there despite what she seems to think, or would like to think.
Re the cats - if she has allergies then yes, make some concessions about that, but simply not liking them - no. I like dogs okay (have been bitten 3 times) but am not a "dog person" so to speak, but I certainly don't expect people to put them away when I come to visit. And you're right that when you have so many people over the cat will probably disappear anyway (mine does the same thing).
She's being
extremely unreasonable to expect you (or anyone) to have toys for an age group older than your child. When my older son was a few weeks old we formed a group like yours. Most of the mums' had new babies' too but one lady had a 4 year old as well. She never expected us to provide toys for the older child at our gatherings - she always brought her own. Really, how much trouble is it to throw a Barbie or a few toy cars in a bag for the older child? It's like assuming that because someone has a swimming pool they are obliged to have dozens of spare swumsuits on hand in a variety of shapes and sizes in case a guest wants to have a swim.
Personally, I wouldn't say anthing else to this woman about the potluck and if she turns up at the next playgroup or the potluck then she does, but if she doesn't then I wouldn't worry anymore about her. How did you find out about all her complaints anyway and what do the other mums' in the group think of her? This woman needs to get over herself.
There always seems to be one high maintenance person in a group like this, but it's been my experience that they eventually stop coming. With any luck that will happen in this case too.
ETA:
And that makes me sad because she needs support and friends. Any advice? You sound like a very nice person to be concerned about her like this. There was a mum that came along to some of our get togethers and she too needed support and friends due to her situation, but after a while it became obvious WHY she didn't really have many other friends. Her demands and behaviour were unreasonable - she sounds just like the woman you've described. If she needs friends and support she needs to act in a way that makes her needs/wants reasonable. Sometimes you (general) have to just be added to the list of people that the unreasonable person has alienated.