It's quite a leap from "she's a good kid" to "she's sneaking out at night."
You give no other evidence at all of her being a deceptive kid (unless her going out with other dancers and not telling you she ate out with them is deceptive to you). No other signs or signals that she is duplicitous. You are going entirely on a sound you might or might not have heard right (if it woke you from sleep, are you sure it was a car door and not another sound?) and on your MIL's planting an idea that you should be suspicious of your "good kid."
Ask yourself:
Why are you so willing to go along with MIL's planted idea if you have no other reason to distrust your child? And why is MIL immediately leaping to a very negative idea straight off the bat? What's her agenda in being that suspicious of her grandchild?
Why are you more concerned with the planted possibility of sneaking out than you are with the idea that your child might be sick? Have anemia, diabetes, an eating disorder, a horrid menstrual issue, whatever come to mind? I think most parents of a good kid would first think of illness and/or stress -- and would not leap to "she's deceiving us and sneaking out." She might be ill and not even realize it herself.
Why are you afraid of your own child? Why haven't you just said to her: I can see you're tired to the point of exhaustion, and today two of your teachers said you fell asleep in two different classes; so we need to talk about whatever is going on. I won't yell at you or come down on you or be angry; I need to know what's up for good or for bad, so we can get you to a doctor and get you better if that's what's needed.
Why is that so scary to you? Please think hard about why you're letting MIL plant ideas; why MIL is so negative about your child; and why you can't talk to your own daughter. Maybe you're scared to talk because you'll find out she IS sneaking out. But you will just eat yourself up with suspicion if you don't talk with her. Not to her. With her.
Do you have any reason whatsoever to suspect these older dancers, which you seem to do, though you don't say it outright in your post? My daughter dances and every single older dancer at our studio is far too busy with serious dance plus school to be roaming around at night helping younger kids sneak out. Maybe you've heard or seen things that concern you with these older dancers. If so, time to stop letting your child ride with them. But don't bring that up until after you know what is really happening -- it may have nothing to do with those rides or those older kids.
Talk to her immediately too because, well, THAT is why the teachers called you. Teachers dont' usually phone home unless the situation really worries them, and they do not expect you to wait and ponder and go online for advice; they expect you to deal with your daughter and find out why she is falling asleep in class, and they need you to do it now.