Could we replace a custom sliding door ourselves?

With no door or framing experience, I would not make this the project to learn on. A large slider is heavy and awkward to handle, and getting it level, square, and properly sealed matters. If the opening or frame needs repair too, a mistake can turn into a bigger job.

Get another assessment before deciding. Ask what is damaged, whether the glass or panel can be replaced separately, and which parts of the frame actually need work. A single expensive quote does not tell you what the job should cost.

First pin down what “custom” means here. It might refer to the door size, the frame, or changes needed to the opening. Ask a door and window supplier or installer to measure and price the door separately from the labor and any carpentry. Also ask whether a standard unit could fit with changes to the opening, and what those changes involve.

Check with your insurer as well, since the door was damaged in an accident. Coverage and requirements depend on the policy, so do not assume either way. Compare a few written estimates with the same scope before weighing DIY against hiring someone.

DIY can be reasonable for someone who has installed exterior doors before, has at least one capable helper, and finds that the existing opening is sound and close to the replacement size. For a first project with broken glass and reported frame damage, that is a different level of risk. You also need a safe way to handle and secure the opening while the work is underway.

If you do consider it, get the exact door specifications and installation requirements from the supplier first. Do not order based on a rough measurement or assume the old frame can be reused. If there is structural or water-damaged framing, or the opening needs resizing, bring in a qualified installer or carpenter for that part.