It's one thing to say, "I can't afford a vacation right now but I hope you have a great time." vs saying, "I don't have any money! It sounds like alot of fun and I want to go but I am poor!" And hinting for someone to pay. Those are 2 very different scenarios.
If you feed it once, it will keep harping on it as the reward is worth the hassle/whining. A free trip/meal etc. I would simply say from now on, "We are doing this on this date. If you can come, please do." And if she cries poverty, "I am sorry to hear that. Maybe next time." and change subject quickly. If she tries to bring it up again later, change the subject again. Or make excuses to hang up, don't let her indulge her in pity whine etc.
As for calling her out, only your husband can do that. And he can if he wishes. He could say, (after an extended bout of whining/accusations) "If you truly want to come with us on this trip, why don't you save up money for it? We are giving you plenty of notice." And let her be defensive about it. Good luck, I know many people like this and it's truly frustrating.