IF I only had one day, I'd probably stick to one park -especially if you aren't familiar with the parks and their layout. You will lose at least an hour to transfer between parks - figure you've got to walk out, walk to the bus/monorail/boat launch - wait for the vehicle - ride - then walk to the park entrance, go through bag search, ticketing and walk to your destination. And if your destination is a restaurant, they want you there at least 10 minutes early. (MGM to MK is by bus to the TTC.)
That said, we usually don't spend a FULL day at MGM for our family. We can cover the rides we really like in less than that -but we really like Epcot, so we spend extra time there, and its an easy transfer between those two parks. MK and MGM are farther apart. I'm not saying it CAN'T be done. My family HAS gone between those two parks in one day - but we didn't expect to all of either park when we did it. We went with a mission to see only certain rides, and used the bus ride as our "break"/nap time.
It also matters a good deal if you are staying on property, and when you are going. If you are on property - one of the two parks (usually MK) may have either EMH hours or more extended hours (beyond the normal 9-9scedule). IF you went to MGM in the morning, and MK is open until Midnight; 9am to midnight - would give you quite a bit of time. Again, still not enough to do ALL - but quite a bit.
If on the other hand, the hours are only 9am to 8pm close at MGM, and you start your day at MK- you won't get nearly as much done.
It will also be MUCH harder to move during a crowded time of year - like Easter week, or any part of spring break season.
MK has a lot to offer! more than enough for a full day!
I last went to LTT's character meal just after they started offering it. The food was't my personal favorite, but at the time the character interaction was great. We didn't see all the chracters, but they each spent quite a bit of time. I think they've revised their system at all character meals since then though. The food is basic American food, the characters are only at dinner. Personally, Crystal Palace is my favorite in and near MK, but it depends what characters you want/like.
The new character meal is quite popular. If your child likes Little Einsteins, then I bet they will enjoy the meal.
Last, if you want to go from one park to another in the same day, you'll need a hopper pass. For a one day ticket - it's a LOT to pay. If you are ONLY talking about two days tops - then it's probably worth it to pay for a second day and not pay for the hopping feature. Still, if you only do two days - you'll be missing Animal Kingdom and Epcot, which are also great parks! the more days you add the more the price drops. If you get a four day ticket, the price of a fifth day is only a few dollars.
Ooh, one more thing. If you do MGM on a second day, and you don't have hoppers and you decide you'd like to leave for a little while (or the park closes at 8pm, and you find you still have energy) you can walk around the Boardwalk area without paying a second admission. From MGM studios, there is a boat ride you can take to explore the entire area between MGM and Epcot. It's really pretty at night! After a big lunch, you can gt a slice of pizza on the Boardwalk or dine at the QS restaurants at any of the resorts over that way.