Nobody said anyone found red shoes in the house on the night she disappeared. What you have totally failed to understand is that Joana wasn't even considered as having been abducted for nearly 4 days. Only after this period of time did the GNR call in the PJ detectives when they realised that all was not as it seemed. Only then did Leonor claim she had been abducted.
I was referring to the statement on this thread - from Carana.
BB1 (one of Leadro's sisters).
Na 2ª feira de manhã (dia 13), por volta das 14h, a testemunha foi ver a BB. Em casa estavam também o AA e o II. Nessa altura a BB referiu-lhe como é que a CC estava vestida e calçada quando desapareceu. Mais tarde, a testemunha deparou com os sapatos que a BB tinha dito que a CC tinha calçados e confrontou a BB com isso, tendo ela respondido que então a CC devia ter trocado de sapatos e que tinha levado as chinelas. Porém, posteriormente, a testemunha encontrou uma das chinelas debaixo do sofá da sala e a outra chinela no quarto. Procurou o calçado da CC e encontrou em casa todos os sapatos, sandálias e chinelas que ela usava nesse Verão.
This is what I think it says (paraphrasing).
Leandro's sister went to see Leonor at the house at around 2pm. Leandro and João were also there. Leonor said what clothes and shoes Joana had been wearing. Later, the sister found the shoes in the house and asked Leonor about it, who said she must have changed shoes and gone out in "chinelas" (slippers/flipflops?). Later, the sister found one of the flipflops under the sofa and the other in the room (not sure which room).
She searched for all her footwear and found all the shoes, sandals and slipper/flipflops that she had worn that summer in the house. UNQUOTE
I'm well aware that it was while before the GNR called in the PJ. That doesn't change the fact that - as instructed by the GNR - LC formally reported her daughter missing the morning after she disappeared.
When she had not been located elsewhere (dead or alive) and did not return - then of course LC would think she had been abducted. That is surely what any normal parent would think - and dread - in those same circumstances.
IMO It was only the GNR who took their time in coming to that same possible conclusion - not LC.
Is there any evidence that LC claimed anything different to 'abduction' during those first 4 days?