We do leave a regular collar on our dogs with their tags on all of the time but some people don't do that. I feel safer if they always have id tags. I assumed that you knew not to keep a 'choke chain/corrective collar' on the dog all of the time or the Halti either, but some people do not know tha! And many years ago we didn't know not to do that.
It sounds like you and your sister are getting to know Hilda very well.
First of importance is to prevent her from escaping since this is a very HUGE danger to newly rescued dogs. I would "double tether her" when she is outdoors, that is have 2 leashes on her with 2 ways to secure her, a "Martingale Collar" is a great training type of collar or a "Halti" collar is also really good, that is a loop that goes over her nose and the dog will automatically turn in the direction that you lead. Also, it is very important to register her with an obedience course and to take it with her, and then do the practicing together between classes. I'll call your Dad tonight. thanks for the great photos and update.
Hilda really is a great doodle name. I am glad you are keeping it, especially if she recognizes it as hers. She sounds pretty lively. We were careful to keep everything we could think of put away until we figured out that our rescue doodle, Clancy wasn't going to chew the wrong things. Ned, our not rescue doodle still gets into the trash if we aren't careful! We use a metal comb so they can't chew it up. We also found that Clancy could get out of his collar so when we walk him we use a corrective collar (some people call it a choke chain). He seems used to this type of collar. We use a Halti when we walk our Springer Spaniel because he pulls on the leash. She is still settling in so you can just give her lots of love for now, but I would take her to a training class. It will help you teach her to do the things you want her to do.
Thank you for the friend request.