That sucks to have that happen while you are away from home. Sounds like USAA representatives went out of their way to try and help you out. Not really sure it would be their job to jump through hoops to accommodate you..
As an insurance company, they are responsible to ensure that your reimbursed in accordance with your policy and possible provide you with a referral to a company that can get it fixed for you. They cannot force someplace to do the work on your schedule. If you don't like their referral, then you are free to use someone else, but then it up to you to do the leg work.
I don't think you would have got half the help from another insurance company that you received from USAA.
I am so very sorry for the delays you encountered. I cannot imagine how frustrating this situation was with your young child and being out of town. I specialist will be reaching out to you shortly to get more information and to learn what could be done better in the future. We thank you for taking the time to share your experience and look forward to speaking with you.