I love gray but not in a childs room , these spaces should be lively and interesting for childrens developement.

If the room is dark there is nothing wrong with using a bright white, especially since children's rooms generally have a lot of color in bedding, toys, games, etc. I wouldn't use a grey tone of any color. Trust your instinct.

In the baby's room I would also use clear colors, not muted. Babies love contrast.

I would do a accent wall. My children have gone through so many different phases. They will find something they love and after redecorating their room. They move on. I have found a accent wall works out great in a soft color. I try to keep it in the same color family so it gives a little contrast but not cave like.

The other thing is wall decals , easy to remove and change as they grow with a nice neutral wall color and the color from the decals

I don't agree with not using gray in a child's room. My nursery was a soft gray (similar to SW Repose Gray) and it was a neutral foil for all his toys and colorful baby things. It was also a restful space when everything was put away, and helped him sleep at night.