In "Relics" (S6E4) how did the Enterprise escape the sun? And why did they have to destroy Scotty's ship?

Question

After entering the Dyson sphere the Enterprise was forced directly towards the sun of the system and could barely escape flying directly into it with the crew coming to the conclusion that they could survive for maybe three hours and couldn't escape.

But when Scotty and Geordi opened the gate to the sphere again, the Enterprise could suddenly maneuver again and fly towards the gate with no problems. How did they get maneuverability back so suddenly?

At that point Scotty concluded that his ship holding the gate open would be in the Enterprise's way and would have to be destroyed for the Enterprise to get through. Why did nobody consider simply flying a bit below or above Scotty's ship?

Compare the Enterprise's size here to the picture posted below. It would have fit through the gate above or below Scotty's ship easily.

Answer 1

To expand on @Izkata's answer, the two source images are of different scale (and even the aspect ratios are slightly skewed!).

An overlay of the two pictures makes this obvious. First, though, I added some red and yellow dots in the same place on each image to make comparisons easier, and to aide in my rescaling:

Then I overlayed one on the other, with 70% transparency for comparison sake:

Then I adjusted the scale to be the same (or as close as I could get it--clearly it's not perfect, due to some apparent change of aspect ratio and/or angle of the model during the shots):

And finally, now we can take the Enterprise from image #1 and superimpose it on Image #2 to see that indeed, the Enterprise would have fit through the door if flown at an angle. Although it's a much tighter fit than the image in the other answer would have you believe.

Of course the real answer (out of universe) for why the Jenolan had to be destroyed, is that this is what the script said, and the special-effects team simply didn't portray the story accurately on-screen.

Answer 2

The Enterprise could maneuver again because partial impulse power had been restored, as reported by Riker.

As for why the Jenolan had to be destroyed - just take a look at its size compared to the door. Not only wasn't there enough room for the Enterprise to maneuver around it, they didn't have much time before the Jenolan's shields failed completely, and they only had partial impulse power.

EDIT

Using the picture just added to the question, and the edge of the door scaled to be the same size, here's the Enterprise superimposed on the image above:

Yes, that appears to be a much easier fit than the Enterprise ended up having. However, keep in mind my other two points:

• The impulse engines weren't at full strength. The best analogy I can think of is a boat, where you can only turn the wheel an inch or two: You might end up going in the direction you want, if you had enough time and space.
• They didn't have much time before the Jenolan was destroyed anyway. If the door continued closing while the Enterprise was in that position, they definitely wouldn't have made it.