Gotta say I’ve never heard of a push gift. I’m a woman who has had a child. Gotta say it’s quite possibly one of the dumbest things I’ve ever heard of. Sounds like nothing more than a cheap consolation prize in lieu of the actual gift of stepping up to be the best father you can be, being the best husband you can be (now with a partner you share a child with), and being a base for your partner so they can be their best selves too. Like she does for you. Best to you both. You should make a thing of that first hot dog. Much more meaningful