Reading the whole article it seems they are in discussions with the club and beleive it can be sorted out, so perhaps the lawyer is just trying to apply pressure. They are probably in this position because they didn't like the way the trust was going to be set up or administered or something, which could mean they wanted all the money at once and City said no, bu there is obviously a difference of opinion.
But to be fair CCFC have no obligation to the family what so ever. That may sound harsh but it is legally true. If they said they'd set up a fund then they and the family needs to agree on things. They should know that going public with this kind of crap will not impress VT one little bit, it's more likely to push him the other way.
Bear in mind it was not City's fault he died.