I know what you mean and I think you are right. She is not interested in you anymore for whatever reason. I suggest the whole coat-it-in-sugar approach because crazy-neighbor lady might be loopy enough to bad mouth you around the neighborhood if you don't.
On the other hand, I like to give people the benefit of a doubt. You never know what might happen when you ask her what her problem is.
Putting myself in your position: because she is not "friendly" anymore, I would not be comfortable sending my kids over for a visit when I was no longer welcome in her life. It's just too weird. You would effectively be sending your kid off to visit a stranger (disclaimer - I don't have kids).
This is a stretch I know, but if there is way that you can put this back on the mom instead of the sitter ("Instead of bringing baby over to your mom why don't you grab your mom and have her stop by over here. I haven't seen her in ages! and Baby is close to lunch time/nap time/tired/has an ear ache/going through a phase, I wouldn't want Baby to be too much trouble/fussy/etc. over at your mom's") you might break the sitter of the habit of asking. She likely knows her mom won't come over so if you lather, rinse, repeat, with the excuses you might get to keep your sitter and lose the mom.
Just a thought.
ETA - I am assuming that the sitter is asking to bring the kids over to see her crazy-neighbor-mom because the mom asked. If this is about the sitter wanting to show off the kids and her responsibilities and the mom is not all that interested in the kids then the excuses idea still applies only to save the feelings of the sitter.