toddler and baby on the way

My daughter was born premature so I guess it made me spoil her more (holding her, not putting her down) and I say now it's biting me in the ass! she has her moments when she's teething badly and she fusses a lot, I still put her to bed from time to time but other than that she's been really independent. I'm having trouble with trying to get her to go to daddy more and it doesn't make anything easier with the fact that she's a police officer and always on call at night. I'm due in August but I will probably deliver in June or July. How can I get her to not be so clingy? I'm a stay at home mom and have been since I've given birth to her and im hoping to put her in day care so that she's around different faces (teachers) and kids.. I point to my stomach and say baby but she's only two and will rub my belly for 2 seconds before using me as drums