I am firmly in the camp that meeting up in Exeter was no coincidence and that Lucy had schemed to bring it about for all she was worth.

Edward couldn't have told Lucy anything he personally knew about the Barton Park people, because he hadn't met them yet when he left Plymouth--but he did know their names and where they lived, since he went there next.

I also think it's very possible that they are no relation at all to the Jennings/Middleton family.

Here's how they met:

In a morning's excursion to Exeter, they had met with two young ladies, whom Mrs. Jennings had the satisfaction of discovering to be her relations, and this was enough for Sir John to invite them directly to the Park, as soon as their present engagements at Exeter were over

Just after that, we are told that Lady Middleton 'had never seen them in her life.' If they really are cousins, and given how much Sir John loves to invite people to Barton, it strikes me as very odd that they have never been invited. How does one 'discover' someone to be a cousin?

Lucy obviously had to know people they knew or to be able to drop names convincingly somehow. She's very clever, and her uncle's school was full of young men who were the sons of wealthy families. I have no doubt that she could claim to be related to someone who is related to someone, etc. 'Cousins' certainly does not necessarily mean first cousins. They might be cousins of cousins etc.--or claim to be.

Barton is only four miles north of Exeter. Chances are they went into the city on a fairly regular basis. We know that Sir John belongs to a club in Exeter that he is obliged to attend at times.