There is nothing wrong with connecting the lines together, it's based on your preference and future planning. 1.5 inch pipe is acceptable and you can tell the plumber that you want 2 inch rigid. They use flex because it's easier for them. ( you're paying, so get what you want)
trenching isn't hard, but it isn't easy either! IT IS Dangerous if you don't know what your doing.
I wouldn't make any permanent decisions until I had the water level down to my planned working height, then trench ( call dig safe first!). Then decide on how to proceed. If it's 20 years old, that explains the not having 2 drains or not connected to skimmer.
I'm not a plumber or pool builder- just a DIY guy.
Are you partially draining the pool or ?
You don't have to remove the drain unless you can't remedy the entrapment issue, if you have access to the skimmer and are re plumbing it, you could connect the drain to it.
I would think that cutting the drain line as high as possible (close to water line) as well as putting a weighted upside down bucket over the drain, you might be able to tie in without losing to much water. I would only do this after skimmer tie in was complete and ready to accept drain tie in.
The bucket my thoughts - (rubber bowl larger than drain) or any brand 5 gallon, add a towel or cloth of some sort to the lip. Then get in pool and put bucket or bowl over drain, set a concrete block on top of bucket. Complete skimmer tie in, cut main drain and connect.
Sounds way easier than it may be, or it might be a snap. Honestly you won't know until you get there.