Thursday, Kate Hudson and Alex Rodriguez went apartment-hunting in New York. Much like Ryan Reynolds and Scarlett Johansson, they took pains to avoid being photographed in the same frame. But it’s pretty clear that they are getting serious together, especially since the couple that apartment-shops together, stays together… for a little while longer, at least. Since Kate was wearing a fabulous blue coat (I want it), we can’t see her alleged baby (or beer-and-hot-dog) bump.

Meanwhile, In Touch Weekly is reporting that A-Rod has introduced his daughters (with ex-wife Cynthia) to Kate, and it’s a love fest amongst the girls. This, of course, is pissing off Cynthia:

Kate Huson’s romance with baseball star Alex Rodriguez has helped her fulfill one of her lifelong dreams - having a daughter!

Although Kate worships 5-year-old son Ryder, a pal explains that she has always wanted a little girl, and she has quickly grown close to A-Rod’s kids, Natasha, 4, and Ella, 17 months.

“The girls love Kate, and she’s especially bonded with Natasha,” the insider says. But Alex’s ex-wife Cynthia isn’t so thrilled.

“Cynthia knows there is nothing she can do to keep Kate away from her daughters, but it is painful,” says the insider.

It will likely only get worse for her: Kate, A-Rod and the kids were spotted looking at houses in the $10 million range in Malibu on September 24.

[From In Touch Weekly, print edition, October 12 2009]

Allegedly, Cynthia Rodriguez was much more upset over his relationship with Madonna - Cynthia hasn’t said a word about Kate, so far as I’ve seen. My guess is that Cynthia’s silence speaks volumes - if she’s not out there giving interviews about how Kate is a succubus, Cynthia is probably okay with the relationship. That being said, it does make me uncomfortable when a girlfriend or stepmother uses the kids as some kind of “aren’t we such a happy family” prop. In Kate’s case, I don’t think she is. In Touch had two photos of Kate with Alex’s girls, but those are the only photos I’ve ever seen. The bigger issue, in my mind, is how quickly Kate introduces her latest boyfriend to her son, Ryder.