I forced them to take me there. If they didn’t obey me, I threatened to blackmail them. So it's not their fault. This is solely on me. Fault is uncountable when it is done my a person or group (plural peoples) Faults plural are countable when you are referring to many faults. "it is one of his many faults" = he has more than one fault (plural faults) "The San Francisco area has many faults in the ground" referring to the earthquake faults (cracks in ground)in that area. "The tennis player lost the match after committing many faults" so we say it is his her their fault, unless we are being specific in describing their individual many plural character faults. You sentence refers to them (they) not being at fault a singular fault. "it is not their fault collectively". Hope this helps to explain why for your sentence we say "it is not their fault"

The only change I would make to your sentences is 'their fault', not 'their faults'. Someone who is smarter than me can explain why we use the singular form of 'fault' here. The tense in your sentences sounds good to me.