Is the wife's mother to be held accountable for taunting her with the swindling, thieving brother of the wife? Is the wife sinful for what her brother does? And is it permissible to say "Hasbiyallahu wa Ni'mal Wakeel (Allah is sufficient for me, and He is the best Disposer of affairs)" in this situation?

If the situation is as described, then the husband’s mother is sinful for taunting your brother and harming you. She will be held accountable for that unless she repents sincerely, followed by seeking forgiveness from you and your brother. You are permitted to say, “Allah is sufficient for me, and He is the best Disposer of affairs,” because it is seeking refuge in Allah and relying upon Him, and you are in the right.