Great-Grandmother Problems

Does she give a reason for these last minute visits?
If not, I would warn her in a nice way that you need to put her visits on your calendar to avoid conflicts. Otherwise it will be catch as catch can.
Next you need to break her of asking what you are doing that you cannot cancel. This is done with firmness and generalities. Instead of, "I made lunch plans with my old friend Linda," you might try, "I am sorry but I made plans for Friday weeks ago." If she inquires further, be ready to change the subject in a friendly way. Perhaps you can even mention the two of you planning something for her next visit. It sounds like you have a fairly good relationship with her, but do not assume for one minute that whatever you tell her is not going to get back to your ex. It will no matter what she might be telling you. Count on it.
You are young and this is all part of taking control of your life and making it go the way you want it to, but I am impressed that you have maintained relations with his family. That is great for your daughter.
Good luck,
C. S.

M. - first I want to just let you know that I admire you for being strong and taking care of your daughter and Mom at the same time. To try to answer your question, I'd say to stand firm for tomorrow and do not change your plans. When she asks you what you are doing, just say "why do you ask?" or "something personal" or "I have an important appointment." Be vague but just make it matter of fact and then change the subject.

Having said that, it's great that she wants to be involved in your daughter's life, which you indicated you totally support. I'd like to suggest you be a little more pro-active about getting together with her. Why don't you call her up every once in a while and say "hey, it's been a week since you've been here so I figure you must be coming soon, we don't want to miss you again, so when are you coming so I can try to plan for your visit?" Also, why don't you just invite her for a visit on a specific date and then hopefully she can plan to see her other family around that - again, at least once in a while. Also, she can come to your house and visit your daughter so you don't have to leave your Mom. In general though I'd say if she gives you some notice and you can change your plans, try to accommodate her SOME of the time because it will be important for your daughter to grow up with people from her Dad's side of the family, especially if her Dad is not involved in her life. To reiterate though, don't change your plans for tomorrow, just politely decline and say how disappointed your are that you and your daughter won't be able to see her.

I have had this issue with my own mother. You must set boundaries and you do not owe an explanation (this will take practice...lol).....I just say 'I am sorry but now/today/tonight is not a good time for me, I work on a schedule with all I do and would be glad to put you on it too'. I am a single, homeschooling mom of teens with busy schedules. If it works for you, go when you can but I never change my schedule anymore......it is a difficult situation, I know, as I was there and my ex learned his controlling behaviour from his mother. He is deceased now and I am in contact with some of his sisters again. Kids can grow up just fine with only one family (mom's or dad's)...mine have....good luck!

Can you see if she would babysit at your house rather than going out to lunch? You could do your own thing, even if it's only for an hour or two.