Decelerate to collect, wrap with arm/hand low so as not to cue the dog to take the jump, and use eye contact. I would not make the cross... why burn yardage in this situation when you don't need to? And, by front crossing, and then having to rear cross the tunnel, you're just creating more work for your dog... and I think staying on the same side presents the nicer line for the dog, and there's no need for a lead change for the dog. If I have a dog with a tendency to want to go out and take stuff, a name check would also come into play (the number of decel cues depends on the dog), and then accelerate and send to the tunnel.
On your first video: you mention the wide turn. I think the reason it is happening is with the cross you are making, you are giving her yardage and she is taking it. I think the wrap with decel and no forward until she has taken the jump, collected, and turned would help to tighten her up. Also, I can't tell from the video because of the angle, but be careful of how much forward you give by how much arm you use to send. You'll also want to experiment to find Lexi's commitment point. If it's very early (and I assume it is), you need to start your decel earlier to get her to collect so she doesn't waste yardage. Those are things Linda Robertson pointed out to me when I went to Murfreesboro for a private lesson with her recently. I was having problems with wide jumping... and those were some of the things that helped to fix it. Immediately I saw improvement.
In the second video, you need to send earlier so you can be further down stream to make the push a little more seemlessly. If you were ahead more, you wouldn't really have the tunnel entrance open as an option, as you would already be around and pushing out for the tunnel.I think it would be a good choice on course if you are pushing for time, as the first option you tried burns more time, while due to the push over the bar, you would be saving yards by making your dog collect more. This second option, if you needed to get downstream quickly would allow you to be in a better position to get there more quickly (but again, you've got to be on it, and ahead. Otherwise, you aren't saving the time/yardage you're pushing for).
That option on video two would also depend on what works for you and your dog. My Athena will burn less yardage, and drive better with the push than playing around with crosses and wraps. I can FORCE a tighter path with the push. I can FORCE her to collect more. The reason is that I can be ON the bar there, and it's either collect, or take the bar or land on me. You need to experiment and find out what your strengths and weaknesses are to see what's most effective... and then train the ones that aren't nearly as strong. All skills will eventually have their place on course.
We did something similar at Linda's where there was a two jump serpentine headed slightly back toward the first of the two jumps down a straight line of jumps to a tunnel entrance kicked out kind of like the set up in the video with the entrance almost directly in front of the line of jumps. The push was the best way to get ahead and get downstream to keep them out of the wrong tunnel entrance, and beat them down the line.
My dogs are faster than me. I should hit the gym. I'll try to set this up and see what the dogs (and I!) do!
