K.K.
No I don't think you were wrong to ask that, but I would not call her to ask her about it bu that is just me, unless you can do so VERY diplomatically and do so reassuring her that you are not interested in him but just need him to do his fatherly duties. I guess one way to deal with it would be to tell him if he is not willing to put it back in your car, he can buy a seperate car seat for himself (especially if you bought this one) so you won't have to transfer it.
This is a hard situation and you have to do what you can to try to not make it any harder. Sounds like he has a jealous, immature girlfriend, but then again, maybe he is just using this as an excuse and he is just lazy. You don't really know and either way he is wrong for not helping you with this as a single mom - but you also have to take the "high road" and think about the atmosphere around your daughter. You want to stay on as good a terms w/ her father as you can. Maybe talk to him about it at another time and explain the need for you to do this and ask him if there is any way to fix it - pray also and ask for guidance and strength, as I feel for you so much.
Keep on girl, you get the benefit of having your daughter so don't let it become a hassle, it is not worth it.
Take care,