I would respond with "I'd love to, thank you for thinking of me but I just got my nails done." IF you do want to see her, suggest meeting for a coffee instead? You can buy her a coffee, see if she's looking for something or maybe, just maybe she does really want to spend time with you and fix the relationship.

It's an olive branch don't toss it aside until she tries to hit you with it.

No. It is your good natured heart that is hoping this will be a bonding opportunity. Your common sense has already told you that she is just using you. Stop letting her use you. If you let them use you, they will keep it up until you have nothing to give then they’ll find a new supply leaving you wondering what happened. Save your money and effort for when she actually deserves it and wants to spend time with you getting your nails done. As a teacher I can’t tell you how many students I hear complaining about how terrible their stepmoms are then within the same class period talk about that same stepmom took them to get a fresh set of nails or new expensive shoes or to get their hair rehighlighted. That’s YOUR skid too. Stop playing the atm, the desperate to be liked stepmom, the Disney parent and teach the girl the lesson she should have learned years ago: you get what you give! 

Don't do it, because you are just going to come here and complain about it. I just read through some of your past entries and I don't see what the point is. You don't seem to want to maintain a good relationship with her. 

I personally would go and get a pedi, but I actually like spending time with my stepdaughter. You keep saying you're going to disengage and then you don't and then you make posts complaining about it. You either try to maintain a relationship with your SD or you don't. But you seem to be annoyed by every childhood thing she does, so what's really the point? She may be asking you selfishy, she may be asking you because she wants to spend time with you, but does it truly matter to you? You take her and you'll be making another blog entry about how awful she is because you took her to get a mani. 

I actually do really think you should go and try to maintain a relationship with her. But you can't disengage and do that at the same time.

Um she wants you to take and pay for her to get something done on YOUR birthday? Uh no...

I would recommend politely declining. Most likely she's just using you and going with her and expecting things to change or her to be appreciative is just setting yourself up for upset, frustration and regret. 

I would check with DH and ask if he had anything to do with this invite.

Why is it impossible that she just wanted to do something nice with you?

Wholly cow, some of these responses....

She's a kid trying to connect with her SM with something she knows the SM likes. This relationship is never going to improve if OP jumps to conclusions and projects every step of the way. 

Stop putting the wicked in stepmother. 

What do you want out of the relationship with SD? I mean, what do you really want? Do you want to be two people who happen to be related to the same person? Do you want to have a mother-daughter type of relationship? Do you want an aunt/niece relationship? Do you want to hate each other?

Your perception of SDs motives everytime she communicates with you will deeply influence your relationship with her. Rather than guess that her motives are selfish, maybe just go with it. Fake it til you make it? If she is hurtful toward you, have an honest talk about how that influences your relationship and move on. Try again if you want to, if not, don't. But don't make assumptions about her motives until you drive yourself crazy.

And if DH did put her up to it, GOOD. He's parenting. Teaching her to think of others and reach out when she's made a mistake. She needs that so much.

The OP has posted about SD's mom and grandmother sending her gifts/cards for her birthday and Mother's Day. (The OP posted some snarky comments about those kind gestures.)

Perhaps one or both of them encouraged and provided the funds for the kid to do something nice for the OP.

While this BM may be rough around the edges, she isn't the crazy, shit show of a BM many posters here are stuck with.

This poor child.  

Hm.  Well, this is tricky.  Been there, done that AGAIN. 

My OSD would do things with me, or DH or the both of us only if she wanted something out of it.  If she didn't directly benefit she would not. I mean outright raging, yelling refusals.  Sometimes, she would try to call the shots as well.  Example, I told her that I would take her out to lunch or dinner once a month, just the two of us.  She readily agreed because she loved going out to eat.  We did it one time.  Then she started not showing up at our home any longer.  The last week she was at our home, a month after our "first dinner" (I hadn't brought it up again because she was being truly horrible and had no idea if she was going to show up or not) she asked me if we could go to dinner on X day at Y time (basically the next day).  I said no, because I couldn't give work last minute notice to leave early due to the time she wanted to meet but we could go to lunch that weekend.  WELL - that was NOT going to work because BM was going to meet her after dinner (to take her back to BMs I think, so she wouldn't be at our place after all on the weekend).  And that was a for sure, "I am not chaning my work schedule last minute for you.  If you want to go to lunch this weekend that is fine, but I cannot do it tomorrow."  Because that dinner meeting was just a plan to be in a convenient spot for BM to pick her up, nothing more.

I would be concerned about the way she phrased it, for your birthday. And are you paying for her to get her nails done for your birthday?  I might try to negotiate and see how she takes it.  Would another weekend work better for you?  Let her know that it's nice of her to ask, but that if she could do it with you maybe 2 weekends later that would be great.  If she truly wants to do it for you then this would still be a good deal...if not, she might throw it back in your face.