It is always difficult to make these decisions. However, the reality of your mother's health problems out-pacing your abilities to care for her must be accepted.
The best thing to do, and it looks like you have, is to investigate the facility - both with visits and online with state and federal rankings. (I don't have any links but a Google search should help you find them).
The one thing to help your mother once she has moved to the nursing home is to visit often (and be sure to see the administrator and other staff heads (activity director, nursing director periodically - hopefully just to say hello and thanks). Not only will it help your mother with the transition but when staff realize you care a lot about your mother, they tend to be more attentive to her also.