Wow- you are the nicest Stepmom EVER. Seriously, lol. My husband and I have a good working relationship with my ex and his wife, but I have never taken my son to get his father a gift. I have always just sort of felt like that was his stepmom's department and even something they might enjoy doing together. In reality, she does not take him anywhere alone, although they get along well and he is almost 11, so not little and difficult to shop with. But she only really interacts with him as a 3 part unit when his dad is there. His father actually gave me a hard time once because the school had made a Mother's Day craft and he had not also received a Father's Day craft! So you are really going the extra mile, IMO.
But enough about me- This is hard, because you do not want the giving of the gift to be something that ends up HURTING your SD's feelings and it sounds like that is what is happening. Even if you have a decent relationship with the mom, this would be very awkward to bring up.
What about a gift card for something your SD and the mom can DO together? A jewelry making class or cooking class or one of those Paint a Pot places? That way it is a gift- but something that she and her daughter will spend time DOING? That might help the mom accept 'ownership' of the gift a little better.
It sounds to me like possibly the mom is uncomfortable with the gift because she knows that in a sense it is coming from you. I am sure she knows you mean well, and wants to make her daughter happy, but at the same time, we all have those weird little jealousies that are hard to get rid of and sometimes they flare up in ways that we don't mean.
You could talk to the mom about how her daughter's feelings are being hurt- but she is likely to just think you are 'projecting' or trying to guilt her or make her feel bad. (I know you are not, but I think that is how it would be taken, unfortunately.)
Do you have ANY kind of relationship with any of your former in-laws? A grandma or aunt etc. that you are not on bad terms with? If you do at all, I would approach them and very delicately explain the situation.
Just make it clear that this is about your Stepdaughter's happiness and wanting to give her mom a gift and that you feel that the mom is just feeling it is awkward because you are also associated with it. You could even offer to still pay for the gift- but see if an aunt or other relation would be willing to take your SD shopping for it and make sure that the mom knows that is how it went down.
Good luck- these types of situations are always sticky and people cannot help bringing their own emotions into it. But as I said, you are a GREAT stepmom for putting so much thought and effort into this issue and helping your sd out this way. It seems like the least her mom could do would be meet you halfway, but maybe she just can't see it from that perspective. Please let us all know how it works out!