What can I say to "I'll check my schedule" to get a more definitive response?
If I may, I would reframe the question as,
What can I say to avoid getting an "I'll check my schedule" response?
... to which I would answer:
Set a deadline.
Simply add, "RSVP by [date]" to the event invite. At that point, it is assumed that everyone will "check their ...
I'll check my schedule.
In other words: "I don't know yet if I'll come, but I don't want to say NO right now".
Possible causes for that answer are:
I'm not sure I'll have time.
I'm not sure I'll enjoy this.
I'm not sure I can put this on top of my priorities.
...and so on...
The other person may think that it's none of your business to know the real ...
I understand how this feels, and I've been the person that says that they will check their schedule. I also often forgot and had the other person remind me.
What I can say, it helps me to let me know why you want an answer now. If you do that, you create some sense of urgency with the other party. If you didn't, then I would indeed forget.
Two situations ...