I'd change the color of the subtext, the contrast is too low against a white background.

Regarding the type of organization, I'd prefer a softer main colour. Magenta is kinda harsh to me. But that's something personal.

The text in italic and the logo are now leaning towards each other. Is that what you wanted? Maybe you could make the logo a bit more upright.

Over all, it looks quite calm and neutral. Which is good, I suppose.

With a quick look, I feel that the modified G on the right might be improved by removing the perspective distortion on it that now makes it slant back and to the left. It seems like an unnecessary additional feature.

You could also play with making the ends of the G sharper to make the shape's identification with the letter, not just the graphic of a head, clearer. Possibly making the left side of the arrowhead bigger than the right side might help. As is, it took me a second to realize that this was a face and a letter.

Also, to help with "reading" the G as well as a face, you might rotate the G so that it looks more typical, with the face slightly looking up. That could also be suggestive of the organization: looking up toward hope.

Maybe the star could be in the same color as the subtitle ("for domestic violence and abuse") to unite the image?

And I agree with all of Jorik's suggestions, especially the angle of the type and the G.

I agree with Jorik and Reed—if this logo is going to appear on white on a regular basis, it's a bad idea to set the second line of text in yellow, as it's going to result in that text being illegible much of the time. And unless there's some good conceptual reason for the perspective effect, it doesn't need to be there.

I'd lose the either the cross or the arrow in the big illustrated G. There's already a lot going on in that logo as it is, adding either of those really pushes it over the top. The arrow pointing up gets the point across on its own, if the client really insists on sticking the cross in, pointing at it is just too much.