One consideration is whether you can document that the landlord's agent (his daughter) knew that you would be moving in with three dogs, whatever the lease may say. Another consideration is whether you can document that the landlord or his agent had actual knowledge that you had three dogs in the rental, and how long they were aware of the presence of the three dogs. If you can prove that the landlord gave permission for you to have three dogs, or knew about the dogs and didn't object for a full year, you are in a good position to assert that the "one dog" provision was waived. No matter what the lease says about outside agreements, a landlord's ongoing permission to have three dogs in the rental unit would constitute a subsequent waiver. And even if a lease includes a nonwaiver clause, there's authority in Texas that a nonwaiver clause can itself be waived, and for the assertion of an estoppel defense against a party seeking to enforce a nonwaiver provision.
On top of that, even if you cannot prove that the landlord or his agent had any prior knowledge of the additional dogs, you have the question of whether having three small dogs would be deemed a material breach of a lease that permits one. A material breach can be grounds for eviction, but a minor breach will not ordinarily permit that strong of a remedy.
The big question, though, is whether your landlord is going to play hardball and actually try to evict you over the dogs. If so, it makes sense to consult a lawyer who offers eviction defense services. (If you qualify, legal aid typically offers that type of service and, if not, they can often refer people to lawyers in the community who offer those services.)

