Boy, I don't know. those things seem to have pretty iron clad contracts. I
would definitely move.

Do others in the complex have more than one cat? Does the rule also
say no more than one dog? Do others in the complex have more than one
dog or other animal?

These facts could help the negociation. If they are not enforcing it
uniformly, that can be grounds to win against them in court. Are they
telling her that she is not in compliance or is she simply worried
that they will when they find out? If it comes down to it, they might
not want to go to court over this.

If they do go to court, she could try asking to speak to the governing
board of the complex. They MIGHT grant her an exemption for the two
that she has if she promises not to get any more and not to replace
those when they die.

I would write a letter to them offering this if they do sue her. A
judge MIGHT say that her position is reasonable enough that the
complex should settle for that. Actually though, the complex does not
have to back down if the board of directors does not want to. It is
really up to the board to enforce the contract or not. If they say
yes, there is little you can do except fight it in court.