I can see why you would feel left out. It does seem to be unbalanced.
Just because you were there first doesn't mean that you should be primary however. To me, having a child with someone automatically makes them primary in terms of responsibility to up hold connections for the child, but not of hierarchy. I wouldn't try and use that as leverage here as it likely will fall on deaf ears and might be more of an irritant than anything else.
I would wonder how you have been addressing your needs. Have you all been sitting down to discuss how to create a balance? Is there a compromise this early in the living situation that is not worked out yet? Its only been four months. For me in my living situation, it is 7 months. It has taken time. For us though there was no cheating and no babies involved. Cheating situations might take longer in terms of gaining trust again... perhaps this all happened too early. I'm not sure I understand why this woman had to move in, could she not of dated your partner and lived elsewhere? As for babies, they are a lot of work and I'm not sure any of you would have the adequate amount of time to spend on the communication necessary to make living together work.
It could be that your relationship with you partner is over. Maybe you could check in with your gut on this and even ask her if she thinks so. It sounds like she is stringing you along to me.
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