She has a lot of pain due to arithitis and limited mobility, so she avoids leaving the house. Getting in and out of the house is difficult. All The locations must be wheelchair accessible. Falling down seems to be a great concern. She will cancel Doctor's appointment, because that means leaving or house.
Has she been diagnosed as being disabled, and is she getting disability payments? I assume she's not working?
As to the other issues, is her limited mobility due to arthritis or other issues, such as diabetic neuropathy?
If you don't have ramps, contact your local community and inquire about HUD funds for emergency repairs. Also contact Habitat for Humanity and Christmas in Action, both of which make repairs for income qualified people. Some churches do as well; you might call 211 to ask about this.
Wheelchair ramps must be installed according to local code, which specifies a certain pitch for the ramp, so it's a good idea to have a charity such as Habitat because they've dealt with these issues before.
Are you her primary driver, and if so, can you physically handle taking her to medical appointments and putting a possibly heavy wheelchair in the car? If not, there are medical transport companies that can help.
Contact your Area Agency on Aging for information on these transport companies. Your sister should not be cancelling doctor appointments given her condition, but rather finding ways she can get there safely.
There are a lot of ways to adapt living space to avoid falls. Ask her doctor for a script for home PT, OT and nursing. They'll be able to make suggestions how to adapt your living arrangements to help her and offer therapy to strengthen her as well. They can also provide information on assistive devices such as grabbers to help pull on socks and trousers.
If it is the anxiety keeping her in, the worst thing she can do is not leave the house. Agoraphobia grows stronger if someone doesn't work on it. Encourage her to get outside, if only for short trips up and down the block. Agoraphobia and panic will usually clear within a few months if someone is working on it. There may still be anxiety, but at least it won't be crippling.