?? If she doesn't like what birth control does to her cycle, why not just use condoms? Is she really prepared to raise a child with someone she's only known for a month, who could turn out to be very different than she thinks? That seems deeply irresponsible to me.
Yes, it's ok for her to love him, no it's not ok for her to let that fact make her act like a fool. It sounds like she's deep in what the poly community calls "nre" or new relationship energy. There are lots of good articles out there on what it is and how to deal with it without ruining your other relationships.
Regarding the discrepancy in her desire, that is another factor of nre. It's a rush of chemicals and the excitement of newness that make him seem irresistible. The problem is, that can make you feel left behind, like old news. For this to work, she needs to be actively investing in her relationship with you and not putting all her available energy into the exciting new guy. Maybe you two can look into ways to spice up tour sex life, go on romantic dates, etc.
I imagine you're watching the kids when she's out on dates with him. If you get to know him and trust him, maybe he could watch the kids while you two go out on dates too. Or she could watch the kids while you go out and enjoy a hobby of your own. There has to be some balance somehow, is the thing, or you will start to feel resentful in time.
The major players. Me, 30ish bi female. Gia, girlfriend of 4+ years. Clay, boyfriend/dom. Davis, ex/friend/"it's complicated." Eddie, roommate & fwb.
The supporting cast. Eric, Gia's husband. Bee, Gia and Eric's toddler. Dexter, Gia's lover. Helen, Eric's lover. Izzy and Nikki, Clay's partners. Liam, Eddie's husband.