Just my 2p worth:
Well done on handling things so far - sounds like a nightmare! I'm not surprised you didn't want to get dragged into it but on the other hand I do agree that it will only get harder to sort out the longer it is left, so there is a strong argument for stepping in now.
Also, if there are serious financial iregularities going on, it's only a matter of time before the owner of the land notices, especially if it's the Council who as a public body should be making sure their assets are managed responsibly. Steps may then be taken to end the whole arrangement - you could lose the site completely.
re "buying" the tenancy - it is possible to buy a lease from a tenant, providing the lease allows this, which most allotment tenancy agreements won't do. The lease would have to be properly assigned to the purchaser, and I very much doubt from what you have said that this has happened. If the tenancy has been "sold" in breach of the conditions, action can be taken against the original tenant to end the tenancy, at which point your shouty horse lady will no longer be entitled to occupy the land.
If it is Council land, there should either be an agreement leasing it to the allotment committee or an agreement for the committee to manage the land. Either of these should contain terms stating what animals can/can't be kept there, whether plots can be assigned, how the committee should be constituted etc and what will happen if the terms are breached. Useful to know, even if you don't want to involve the Council and risk losing the land.
An advantage of joining the committee is that you ought to have access to all the documentation, which you can then take to a CAB (free) or a solicitor (not free). Good luck, and keep on fighting the fight!