In this part of the book, Miss Bertram, Mr Rushworth, and Mr Crawford are out for a walk and Miss Bertram decides she wants to go into the park and onto a hill (knoll) in order to get a better view of the area.
The gate is locked and they don't have the key, so Mr Rushworth goes back to fetch it. While he's gone, Miss Bertram becomes impatient, and she and Mr Crawford climb over the gate and walk out of sight towards the knoll.
When Mr Rushworth returns he's annoyed that the other two didn't wait for him, and by saying
If I had made any difficulty about fetching the key, there might have been some excuse, but I went the very moment she said she wanted it.
he's saying that if he'd complained about having to go back and get the key then there might have been an excuse for them rudely leaving him behind, but he went immediately, so he feels it's unfair.
I don't see the phrase "made difficulty about" used very often these days, I'd expect to instead see "made a fuss about", though you do still hear people say "made difficulty for", though that has a different meaning, i.e. obstructing or otherwise causing trouble for someone.