If she's holding, then definitely up the praise and make a schedule of her times. She is likely holding until she just can't anymore (except at night - since you're asleep, she likely sees that as an opportune time to go. So she'll go even if she can hold it longer).
If you can work her feeding schedule to get her "can't hold it anymore" point to a normal time of the evening, then she won't have a choice but to do it then. And that should lessen her doing it later because you've been making a very positive thing out of her going outside.
Little dogs don't usually like going on grass. Their legs are so short that when they squat, their bums touch the wet grass. If she'll go on the cement that's great and the best solution. If she won't take to the cement, you can also get a cheap rubber door mat. When you go outside, put it on top of the grass for her to use. Just make sure it's nothing like what you have in the house so she doesn't start using that.