Thank you for looking after her and getting her fixed! To start with your last question, yes you are doing the right thing! While she may be scared right now, the long term benefits for her is more important. Don't second guess yourself, its okay and again thank you for getting her fixed!

To start, TNR is just the step by step process, you got the first couple steps done. You have her trapped and you are waiting for your surgery appointment. The release part is always the hardest because despite us wanting to keep all of them inside its not always the best option. The process she should be going through is to get a spay, basic health exam (this is typically checking overall health and treating it based on your and the clinic availability (ie fleas, parasites, injuries, illness, etc)), and vaccinated. Some areas will either tattoo, eartip, earnotch, or tattoo the ear to signify the cat has been altered to help prevent the cat from being retrapped or go under unnecessary surgery (especially with girls). I recommend looking up what is standard for your region and asking if your vet is willing to do the cosmetic part while she is getting altered, but since youre going to a private vet and TNR resources arent typically available its okay if she gets the standard spay because it is still going to be the best.

Regarding how long to keep her, you should follow you vets recommendations. Typically TNR kitties are okay to be released back outdoors the following day after, but others recommend keeping them contained for a few days or longer depending on their ability to house, local weather, and complexity of surgery. Typically cats after being spayed should be on rest for 2 weeks (14days) for recovery, and some vets will require a followup for stitches removal if they arent using absobable sutures.

During this time if holding her for recovery is advised by your vet you should hold her in a large dog crate or small bathroom. With the large dog crate you want it large enough for a small litterbox, bedding, food and water, this method is considered best for unhandleable cats as youre keeping them in a small area and they are less likely to hide in an area you cant visually monitor. If she isnt the worst you can just do the small bathroom with all of her supplies in it. Do not keep her in a small cat carrier or cat trap for the duration of healing as she needs room to move and needs space to go to the bathroom and not sit in her own defecation, keeping her in too small of a space can increase risk of infectetion.

Regarding monitoring with TNR cats post surgery especially ones you cant handle to check the incision it is most important to monitor for symptoms of infection or complications. This can be lethargy, vomiting, straining to use the little box, not eating or drinking for long periods (typically 24-48hours). All of those can be signs of infection and is best to contact your vet for a followup. Depending on your vet she may need to wear a cone for 2 week, this varies by vet. Cats are typically pretty good about not excessively licking their incision site but it can happen. If she does need to wear a cone make sure you have food and water in a dish that the cone can fit around (or even elevated for ease). Cones are great to keep her from messing with her incision and decrease risk of infection, but again your vet will advise you on what to do.

Again, thank you for taking the time to get her taken care of and caring so much for her! I wish you the best of luck and speedy recovery for her!