DH uses canes to walk, but does not use a wheelchair all the time on land. Our first cruise he did not bring his wheelchair, as he did not think he would need it. We came to realize that the ship sways and rocks, sometimes substantially which makes it difficult for people with balance or walking issues to maneuver safely and comfortably. Well, the ship lurched once and he fell. He did not get hurt or anything, but it was a learning experience. We ALWAYS use a wheelchair for getting around the ship now.
As stated, many excursions are not wheelchair friendly, even tours through
DCL. We have found that more often than not, private vendors are more accommodating, as they only deal with us, and not 40-100 plus other cruisers.
I don't know which itinerary you are looking at, but tenders are impossible for our situation, and may be difficult for your mother. You have to walk (not use a wheelchair) and the ramp is often unstable and slippery. You may just use that port as a "ship day" if a tender port is on your itinerary.
As far as your original question, yes, DCL does have wheelchairs on board to assist passengers if need be. You just put down a refundable $200 deposit. And yes, you can take them off the ship.
Good luck with your decisions. Happy sailing!