Regarding Martha, why didn't they just lie about what happened to her? If she died or they abandoned her, or whatever, why not say she was sick and had to be put down? At least it's a solid answer, and would put an end to the speculation. They even could have made a tearful video/instagram post whatever... you know, "we noticed she hadn't been eating/drinking, we took her to the vet, but she has an incurable dog disease and unfortunately had to make the hard decision to put her down. we're very sad, and will miss her dearly, but we're happy she is no longer in pain." THE END.
EDIT
Just watched that clip from the show. Nevermind, I think we all know Tanya wouldn't be able to act out a convincing lie like that.
In my mind, Martha is being held hostage by Colombian drug lords.