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Security is very high on cruise ships and each passenger is issued with a boarding card for the chosen cruise.No you would not be allowed to look before you booked unfortunately. If people started to have a look before they booked the ship would never leave port.If you chose a room with a balcony your mother should be fine and go on a larger ship so that she would not feel claustophobic, you can take a tour on line of cruise ships to see the space they have to offer. hope you get your mum to go as you will have a fantastic time.
Absolutely No Way would you be allowed on board to look around. If you book a new modern ship like RCI Independence of the Seas - it is so large you will forget you are on board a ship. Why not look at the website where you can see 360 views of the facilites and rooms.
Princess cruises recently offered a chance to go on board Golden Princess and (I think) Sea Princess for lunch at a cost of £25.00 per person. Might be worth putting yourself on the Princess Cruises mailing list. Kind regard.
The only time you can normally get to see around a ship is when it is new eg - we went to southampton to see ocean vilage before it sailed, kind of a guided tour, but I don't see that happening now what with all security. I have trouble being 'hemmed in' too, so the easy solution is - book or upgrade to a balcony cabin, I do this and if flying opt for window seat & extra leg room to.