Why aren't the agencies that are supposed to help transition family members into facilities helping us?

What is happening that is making the move so stressful? You need to tell us what kind of help you are looking for so someone can give appropriate advice.

Transition can be difficult. The facility near my home, offers free lunch with facility coordinator. They take people on a tour of the place. I believe your mom will need time to adjust. Maybe cut back your visits with her to every other day until she settles in. Once she has made friends at her new home, you can cut back time even more

Help her decorate her new apartment with her favorite photos etc

It is not at all clear what kind of help you need. When my friends were transitioning from independent living in their own condo to a memory care apartment, a man from Caring Transitions helped with the move of their furniture and setting it up in their new apartment. Another friend took them out to breakfast and then to have their nails done while the move took place. When they came to their new apartment, we had made it look as much like "home" as we could--the same furniture arranged the same way, same pictures on the wall. They sat down in their favorite places with a sigh of relief and never talked about going back to their home of some 40 years.

It looks like the person is being moved from an Assisted Living to skilled nursing. Big difference. Unless private pay the person will need Medicaid and will be sharing a room. What she had at AL may not be able to take to SNF. Never heard of people who help with transition.