At this point, you don't really need advice as you've complained and have a reply. Without the reply you received, nobody here can help you. Your paraphrase doesn't help one bit and does you a disservice based on what you went through. But, for the sake of others, if you were at the beginning of the process.
You will need to separate involuntary denied boarding (IDB) into those situations where you or your mother held a confirmed seat on a flight, were at the gate ontime (not an issue) and were then denied boarding due to an oversale, from poor customer service.
The former is a simple formula set by law and has nothing to do with whether your mother has a pacemaker. The latter has to do with screwups, e.g. commitments made by the DFW supervisor who told you that you were #1 on the SB list with 2 misconnects on a flight which was overbooked and then almost oversold.
For each passenger delayed more than 2 hours at the destination, the IDB compensation is 400% of the ticket price, capped at $1,350. So, the task is deciphering whether you held confirmed seats and were bumped due to an oversale. The best I see is that a supervisor made commitments she ought not to have made. Nonetheless, at least your mother ought to make a claim for IDB on the flight where the supervisor told your mother she was confirmed (although she may not have have been) as AA will review the PNR for that.
AA (and no US carrier) reimburses for hotels unless the delay is within its control. This has nothing to do with the weather at ABQ/SAF. Your claim for the hotels & food is to your travel interruption insurance. Same thing for what is called consequential damages such as extra wheelchair tips and the like.
Then, there is the matter of poor customer service. Here it sounds as though you were simply sent from pillar to post as flight after flight was cancelled.
The entire IDB complaint if you pursue it should not exceed 3 short declarative sentences. The people who process these things get about 30 seconds for the first pass on them. They also have the details in front of them.
The customer service complaint ought to focus on the total length of time, your mother's age and the screwup by the supervisor.