Weird gift situation--thoughts?

Spacebunny19

I'll try to be brief (not my strong suit)--

BG:  My mom died just before DD#1 was born.  My dad started dating (too) quickly and has been with the same woman now since New Years '11.  They are not engaged and do not live together.  

Now:  This woman is nice enough and if she makes my dad happy I'm all for it, since I feel he's been given the short stick in life when he's almost at the point of retiring and getting to enjoy life with the love of his life (my mom) and she goes and gets leukemia and dies instead.  So there's that.

Anyway, this lady wasn't around when I was PG with DD#1 (my mom was) and now she has extremely generously offered to buy us a stroller (double) for this one.  We hemmed and hawed and kind of insinuated we had it covered (kind of did but it's not panning out) and hoped that it'd be that.

She instead (extremely kindly) came back with an offer to get us whatever else we might need.

So the rub isn't that we don't need anything (we don't need much though) but I feel extremely awkward accepting anything (large) from her.  (A tiny gift for my DD at her birthday or Christmas is fine, BTW, but there's a huge dif between a cute toy that cost $20 or less and a $200+ stroller).  

And that's because my dad goes back n forth between acting like she's already a member of the family and insinuating he's going to end it with her.  If he did that I'd feel super weird with an expensive gift from her.  KWIM?

I explained it to him (including his wishy-washiness about his attitude about her--which, to my knowledge, he doesn't convey to her, but to me,) and I said that it'd be different if they were married or even engaged, and he joked "Oh so now you're on her side!"  (I'm taking that to mean she's been pressuring him to get married.  Not the first time I am aware that she's been not so subtly hinting to him that she wants that, now.)

Am I being weird or overanalyzing this?  At this point, we *do* need a new stroller, and possibly a new car seat if the one my sis is giving to us isn't compatible with the new stroller.  And potentially a car seat base (travel system dealio).  Is it best to just decline to state any particular need and assume that if she wants to get us something, she'll go less expensive (clothing or something cute and small) or give us a gift card (again, hopefully not a high value one) to show her support, or is that being rude by not responding?  Or would you just tell her the truth about the needs and let her buy what she will?  

(I'm kind of hoping she doesn't get us anything at all.)