I wonder if she really did feel it was a threat at the time. It's easy to say that afterwards when he's been charged with murder.
If that's the first question, surely, the next has to be Why? People generally don't feel threatened without reason, it's part of our "flight or fight" mechanism. Very often, the only reason we dislike a person is because we don't know them. Given that Ann, nearest to Jeremy in age, was some 13 years his senior, it's fairly clear they were never going to be bosom pals. I think it's obvious that there would have been strong interest in him -albeit from afar. He was, after all, the "Heir", and as such, destined to be the next CEO. THEIR next CEO. The person their futures were dependent on.
I think we may take for granted that Jeremy's upbringing was very different from Ann and David's. Theirs, from how it sounds, was more of a 'hands on' experience, which, if nothing else, would have fostered their knowledge of farming, and perhaps more importantly, their love of and loyalty to their family's business. I think it's more than fair to say that it's something they knew far more about, than Jeremy, whose own interest in it, other than financial, appeared so little he didn't even bother to go to his local, and excellent ag college, OR spend every available moment, on the farm, learning the ropes. Indeed, it seems that he took every opportunity to do anything OTHER than farm. Nonetheless, there's the distinct impression that he thought he knew it all and their opinion, whilst he may have paid lip service to it, counted for nothing.
If they didn't trust him to do his best for the family business, it would have been because they'd learned that he couldn't be trusted. There seems to have been a huge lack of communication -if Jeremy was disinterested in the future planned for him, his lack of knowledge about it and disinterest in it would have stood out like a sore thumb, although it's possible he may have been more interested in the holiday park- which isn't surprising, given the amount of time he spent away from the farm.
I really don't see the family's distrust and suspicion of him as being any different from any other business, in which employees hold shares, and the business becomes taken over by a 'whizz kid' with no working knowledge of it, and no interest in it, save it's financial value. It's very natural that they'd feel that their whole way of life and their security was under threat. His behaviours, post murders, would have done nothing to allay those fears. Even if we allow that he may have been consumed with grief, his duty, as head of the family business, was to have kept the family in the loop, to have put aside expressing that grief in his own 'unique' way long enough to reassure his family and employees. You asked if the family felt threatened. Do you think there was anything about Jeremy's behaviours -once he thought he was in the driving seat- that would have made them feel their futures were secure?...............and before you say it, I'm aware that it doesn't make him a murderer, but wanting to get his hands on the money to secure his own future, far away from farming, did.