You can still be friendly and cordial without actively maintaining the friendship. Just because you're neighbors doesn't mean you have to be best of friends, even if you were friends at one point. People grow and change, and sometimes they out-grow friendships.
You need to establish and maintain boundaries with this person, not just for yourself, but because this is a healthy behavior that your daughter needs to see you modeling, and maybe it's something you should talk to her about, as well. This young boy sees how his mother uses and manipulates other people, and he's already learning to use this behavior on other people, as clearly demonstrated at your daughter's birthday party. You need to teach her that she needs to be true to herself so that other people won't be able to manipulate her (please, think 10 years into the future when some horny boy is trying to coerce her into sex before she's ready), and she will only believe you and really internalize it if she sees you acting with the same self-respect when it comes to how other people treat you.
has some great advice. You can still let the borrow the high chair... tell her that you and your daughter won't be able to make it, but that you will bring the high chair over that morning or the day before or whatever. If she presses for a reason, say you have a family obligation. And then, on the day of the party, actually take the kids to see the grandparents or something, so if it ever comes up, and someone asks your daughter what you were doing, they'll say something about spending time with grandma. It will take several polite declines, but after 2 or 3 declines, she should get the picture. If she asks you about it, you can say, "It seems like the kids are going through a phase where they aren't really getting along, and I don't really want to force it. I want to respect their autonomy in this respect."
If she asks you to DO stuff for her, just say NO. You have the right to say NO whenever you want, and you don't need to provide a reason. You can just say, "No, I won't be able to help you with that; it doesn't work for me [right now]." If you are pressed for a reason, you say, "I already told you why, it doesn't work for me right now." And if she asks when it might work for you, you can say, "I don't see it working for me for the foreseeable future. I have my plate full with two children and everything else in my life, so I won't be able to help you with this."
I think, for both of these situations, you need some rehearsed responses, which you just need to practice over and over so they will roll off your tongue without you even having to think about it.
Good luck. Let us know how it goes.