IDK if we're actually responding to the OP since this is a necro'd thread and I'm totally new to the hobby and forums. Just in case we are, I figured I'd weigh in since real rockets, especially the shuttle, are something that I do know about. The model OP described would instantly pitch up violently and crash. The shuttle's center of mass at launch was somewhere in the tank, half way up and towards the orbiter. The SRBs were not on the center of mass's axis, so and the only thing that balanced the shuttle was it's three RS-25 engines, all of which were capable of 10 degrees of gimbal in both axis and throttling betweed around 67% and 109% of original rated thrust. Also, the SRBs had pretty serious gimbaling capabilities. In fact, the control surfaces were locked and the RS-25s didn't move much until the SRBs were jettisoned because they provided the majority of the shuttle's steering until that point. To recreate the shuttle in it's original format, you would at minimum need some kind of motor on the orbiter in place of the RS-25s and you would need a pretty good flight controller with an IMU to balance it. Given how light the model would be and the power of the boosters and engines, even a good flight controller may have trouble stabilizing the shuttle. It would certainly need some custom programming. You may need to make use of the control surfaces because they can react faster than an electric motor, assuming an electric motor can even run hard enough to balance out two SRBs. For realism points, the main battery could be put in the tank, although the orbiter would need a payload to balance that out since it would be pretty significant. You could connect the battery to the orbiter with a spring-loaded contact that would help push the two parts away once jettisoned. The battery could also power a parachute system on the tank. The SRBs could use an AA battery for a parachute too, or a time delay between the main fuel and a parachute ejection charge. They would have to be jettisoned during that delay compound burn. It may be possible to continue flying the orbiter after the SRBs are jettisoned with careful piloting and a flight controller. The center of mass would be in the tank so you'd have to fly belly up, like the shuttle, on an arcing trajectory, or tank down. There is no in between until you drop the tank. Either way, you'll need a lot of gimbal. You'd have to roll tank down to drop it.
You could copy the Russion Buran design instead and put the main engines on the bottom of the tank and just make those engines and the boosters very powerful and capable of gimbaling. With that design, the shuttle is nothing but a glider hitching a ride. The fuel stack (tank/engines/boosters) of this design should be much heavier than the orbiter so that the gimbals alone can compensate for the slightly off-center center of mass caused by the shuttle strapped to the side.
A simpler design, IMO, would be to put the battery in the shuttle's payload bay and strap the boosters to either side of the bay above the wings. The real shuttle couldn't do this because the payload bay held... the payload. The tank was there so the shuttle didn't have to carry all that fuel on board. You could easily start with this design, and then move to the traditional shuttle using the same SRB jettison, parachute, etc mechanisms. This design might not need a flight controller either, so it would allow you to try it and prove the concept before buying and risking a pricey controller.
The shuttle just needs a small battery (200 mAh or less, single cell would probably do it; or just one 18560 cell) for the RX, servos, jettison actuators (servos, pyrotechnic, etc), and flight computer.
This is a very interesting project though. If I had the time and money I'd love to see it.
BTW, by flight controller I meant something that could stabilize the vehicle like a quadcopter's computer thing. IDK if they're called flight controllers or computers or what. Regardless, the shuttle was inherently unstable (think F-16, no computer = you don't fly type unstable). I'm not sure if the pilot could take manual control of the shuttle during launch, but I doubt they could have done it without computer stabilization. That's why they had three of the main computers on board.