There is no way i would be giving her away for the day or the night at this age!!!! You are def not being too demanding, guys tend to be a bit funny with such young babies, im sure as Lyla gets bigger and more interactive he will want to spend more time with her, hes prob just really nervous about her being so small and stuff. It is okay for you to feel that he isn't spending enough time with her, i would have concerns too if i were in your position. Try not to stress about him too much, your little girl will grow up knowing she has a loving father