Welcome to the Disability Travel forum,
annamom!
Yes, you will be able to use your own wheelchair to the gate, and it will be gate checked. You will need to get a gate check tag from the agent, just as parents with strollers and car seats do. Plan to take anything that can come loose with you onto the plane - that includes cushions, bags, footrests (if they detach), armrests (ditto). Put a luggage tag on your wheelchair.
My wheelchair is rigid, so I'm not necessarily going to have the best ideas about how to fasten a folding chair so that it will not come open, but it seems to me that an adjustable strap around back posts or the frame under the seat might do the trick. That said, I think most wheelchair users just fold the chair and don't worry about it.
A couple of other items to be aware of:
- if you pre-board with a folding chair, you may be able to get the chair stowed in the cabin if it fits into a closet. Ask the crew for this when you board.
- when you arrive at your destination, do not set foot off the plane until your chair has been brought to you at the door of the plane. If anything goes wrong and you are still on the plane, the crew cannot leave and are therefore more motivated to get things right. Once you're off the plane, you are no longer their problem.
Enjoy your vacation!