Well, first of all, for me I find that sexual desire/need isn't a gauge that gets filled when I have sex, no matter the partner. Having a new partner won't make me want less sex with existing partners, and actually might make me want my existing partners more.
Why? Because sexual desire for me is based on trust, on how well our relationship is going, on how in love I feel. And for my partners to be fine with me having a new partner makes this existing relationship more precious, with more trust, and more love.
While I can't know if she works the same way I do, it's a possibility, and in that case "your" sex wouldn't be cut down, but stay the same or possibly increase.
That's the first thing. Now, for the date, I don't think it's fair of her to want regular date with a new partner, but dismisses the idea of having them with you. Obviously, if she has time she does, so she should have time for you, too. It's possible she wants regular dates with him and not you because of NRE, but still, I believe dates with just you and her would be very good for your relationship and add to your intimacy, regardless of whether sex happens or not. I definitely think she should take care of established relationship as well, not just the new one.
You need to maintain the romance and the love, and dates are important even when you are parents, maybe even especially when you are parents, so you can get out of the house and the stress linked to parenting... Provided someone can take care of your kid, of course.