Conditional with obligation

Hi everyone,

I tried to find this topic because I'm sure people out there get confused same way as I get. I asked two Canadians and they didn't know the right way so I ask your help.

How should I say the following sentence and which part of grammar is it? (I think it's still third conditional?)

I was talking to my husband other day and I was telling him that when I was younger my parents had an accident where they had their car destroyed. So obviously they could have died, but they didn't.

then I went on with the story and I got to the sentence "If my parents had died in that accident, I would have to have gone to an orphanage/foster home?"

Eu queria expressar o "se meus pais tivessem morrido naquele acidente eu TERIA QUE TER IDO para um orfanato", queria saber mais sobre esta estrutura de expressar algo que nao ocorreu +obrigacao,

Outro exemplo:

"If the rent had gone up in our city, we would have (nos TERIAMOS que TER mudado)"

Obrigada