I think you can mix it. You can also talk to your mom and explain that you are unable to gradually introduce this so please alert you to any problems immediately. Your professor doesn't need to know more than "my baby is sick and I have to leave."
You can also consider asking her to give him all the breastmilk you have possible first and some water (at 9 mo, he's eating solids, right?) and save the formula for the very last, so you can see his reaction.
I have done the "pump one side while nursing the other" and "pumping in the car" and "pumping at weird hours" thing. Anybody who says not to cry over spilled milk has never struggled with pumping milk for her child and had it spill. So I totally get how you feel.
So, for today, I'd pump one side and nurse the other all day. Pump when he naps. Even if it's just a few spare ounces, it's something you can give your mom to either use first or to mix. After you nurse him tomorrow AM, pump some or pump one side, nurse the other.
If you are close enough to swing home for lunch or can sneak out of a lecture, I'd consider it.
Kellymom.com may also have feeding tips in their supplementation section.
Hang in there and try not to strangle DH. This is just a bump in the road and you can get through it.