Given that you are paying lawyers and that appraisals cost money, I'd tell them to just wait to pay until they sold, assuming they do plan an open market sale. You aren't in a hurry. Save the money on an estimate and just take your share when it actually sells. It not, I'd see if I could determine an approximate FMV on my own (us actual comps sold, not Zillow's Zestimate!) and if that was close to the number they were offering, I'd just go with that. It doesn't sound like it would be a difference of tens of thousands or even thousands of dollars in your pocket.
But given that they have been shady, if you think what they are offering isn't fair, then push for the estimator, but I'd want to hire one myself and be the one communicating with them if at all possible. It's very easy for someone to mention to the estimator that they want a low number, and then presto! He magically goes on the lower end of the scale. That means you ideally don't even want family to be the one letting him/her in to the house, if avoidable.
