I'd start by just explaining to the car owner that while you don't mind driving in your own car you are uncomfortable driving someone else's car. Make it clear that you aren't refusing to drive your share and mention that of course you drove last time.
Ask her about insurance, she will need to add you to her policy as you don't have driving other cars cover and in any event it is third party only. You would want a copy of the policy confirmation in case you need it for the police/an accident. Remind her that any accidents could affect her no claims. This might be enough to put her off!
Also talk about what happens if you "ding" or bump the car minor damage not worth claiming for, would she expect you to pay, can you afford it, what if you disagree about what to do?. Say you are nervous and aren't used to big cars and would hate to damage hers and cause a fall out. In an unfamiliar car kerbing an alloy or knocking a wing mirror are reasonably likely.
How will she feel if you grind the gears or ride the clutch or whatever? Does she really want to let someone else drive her car?
A four hour drive is a long drive to do by yourself but it wouldn't be too bad if you break the journey well. I'd plan either one longish stop (lunch and a walk around) or two shorter stops depending upon timings and preference. Maybe talk to her about whether she could manage the full drive with suitable breaks and making sure the journey isn't done very early or late.
Does she actually want you to do a substantial amount of driving or is she just thinking about a back up plan in case she struggles? I would be more willing to consider that.
If she is still insisting that you share the driving and you still aren't happy suggest you try her car before making a final decision. Driving a big car isn't really difficult, in fact often they are pretty easy as long as you don't have to park. I switch between a tiny hatchback city car and a massive pick up truck. On the motorway the big car is actually nicer!
If you still aren't happy hiring a car would be a good alternative. At least then you wouldn't have to worry about driving your friends car and could get something you are both comfortable with.