He lies still as she climbs all over him, sticks her fingers in his eyes and mouth and gives him huge cuddles.
Too that's so touching that he loves your DD so much, but please please don't let her do that. Any dog, however gentle and loving, really doesn't want to be treated like that. If she inadvertantly really hurt him or made him jump and he snapped at her, you would feel awful, he would probably be put down, and she could be seriously injured or worse.
Scared dogs who have been punished for growling (I'm not suggesting you have done this, but you said he's a rescue) or are just too scared to assert themselves will often suppress this natural warning. The next stage up the scale is to snap or actually bite. It's so so much better to learn about dog calming signals and remove the source of stress, than to regret afterwards that a dog has bitten, snapped or even growled at your child.
You (or anyone else - I'm really not having a go at you) can read more about calming signals here. I think every dog owner (and their dogs!) would benefit from knowing this stuff, but particularly owners of nervous or rescue dogs.
Some of the main calming signals (signs that dogs use on each other to say 'chill out' 'that's enough' 'give me some space' 'back off you're making me uncomfortable' etc) are
The look-away - direct eye contact is a challenge to a dog, unless you're talking/blinking etc. Watch dogs interacting and you'll see them using this all the time. You can have much hilarity by staring at your dog for a moment and then doing the look-away - do it a couple of times and they'll definitely react.
Yawning and licking their lips - big signal of mild stress, telling you that they're not entirely comfortable or are asking you to be kind and gentle.
If your child is climbing on your dog (this is really not just to you Too) and the dog is looking away with its ears slightly back, licking its lips and yawning frequently, this is an uncomfortable dog. Don't make it use a stronger message!