These are surely CT billing decisions. She can only be liable as the resident of one property – that’s the one she gets CTB for. She might also be liable as the absent owner of the empty one – but you cannot get CTB for owner’s liability.
For CTB purposes, you don’t need to worry whether the billing decision is correct. Just award CTB for the residential tax she is being asked to pay, wherever that may be.
Incidentally, if you are for some reason charging residential tax on two dwellings, I see nothing in the Conts and Bens Act that would prevent the claimant from getting CTB for both. Section 131(3)(a) requires the claimant to be liable for tax in a dwelling of which s/he is a resident, rather like the main condition of HB entitlement (liable for rent on dwelling occupied as home). In the HB Regs it is considered necessary for Regulations to say that a person is treated only as occupying the normal home and no other [Reg 7(1)] subject to five prescribed exceptions. The CTB Regs do not restrict residence in the same way, so if the billing authority thinks the claimant is resident in two dwellings then s/he satisfies the CTB condition for both of them.