
I think the problem is the puppy pads and I would abandon them and go back to basics with the toilet training. Puppy pads teach a dog the exact opposite of what you want to achieve - they teach them it is ok to toilet indoors whereas you need to be teaching your dog that the only place to toilet is outdoors. I would guess that your pup is treating the vet bed as a very large puppy pad.
You need to take your pup out at regular intervals - after waking, eating, playing etc and you might need to set your alarm for the middle of the night so you can take the pup out then too. Put her on a lead when you take her out specifically to toilet so she doesn't think she is going out for a sniff around or a play. Praise her efforts and reward her - treats, a game, praise - whatever you normally use to reward her.
At night I would take her out and reward her going and then quietly return indoors and put her back to bed. You can gradually move the night time garden visit later and later and eventually she will manage to go all night without needing to go out. You need to set her up to succeed rather than hope she might or by continuing to "allow" her to fail ( by not giving her the opportunity to go out during the night )