Well.... how is your Husband, with her?
Does he 'interact' or just talk 'at' her?
Does he play with her?
Does he talk with her?
Does he try and bond with her?
She is a girl... so maybe he, being a 'guy, has a hard time relating or connecting with her... being a 'girl'?
It does not matter how busy/stressed the Husband/Dad is... because, a "Dad" STILL has to interact with their child... not just be 'too busy' to do so.
My Husband, makes a big effort to bond with our daughter... he even lets her put make-up on him and he talks with her and plays with her... with what SHE likes to do. He is not 'distant' nor does he talk to her 'at' her.... he tries his best, to 'relate' to her... and just chit chat about her day etc.
THAT is important, for a girl and their Dad....
Next, maybe your girl is getting more 'attached' to you, because, you are pregnant... and she 'knows' in her little girl mind... that you are preoccupied or will be not as accessible to her, once baby comes.
PREP her BEFORE the baby comes... for the baby. That is what I did, when I was pregnant with my 2nd child. I spent a TON of time, on my eldest... before, her little brother came home... I transitioned her, even while I was pregnant... so that she was not just a satellite floating around everything... once her baby brother came home... PREPPING your eldest... BEFORE baby comes home, is REAL important.
Expecting her to 'adjust' all of a sudden, once baby already comes home, is too late.... so you need to do it before, baby comes home.
all the best,
Susan