Let’s ignore the problems of fueling the thing to get to the moon in the first place, and start at the end. When the Shuttle is in Earth orbit it is traveling at a speed of 17,400 MPH to 17,500 MPH, depending on its assigned altitude. In order to return to the surface, the Shuttle fires its OMS engines for a short time against the direction of travel — reducing its speed oh-so-slightly (about 200 MPH). This causes the orbit to change shape.
The apogee (that is, the hight point of the orbit) remains the same as it was just before the engine firing. The perigee is now reduced to a point where the Shuttle intersects the upper regions of the atmosphere. This is all very subtle stuff.
So, half a world away the Shuttle is rubbing against the atmosphere, and reducing speed and altitude. It gets fairly hot, and the G forces increase — but not alarmingly so. Yada yada yada, you know the rest.
How does an Apollo-type spacecraft return to Earth? It all starts at the Moon. The spacecraft fires its engine to escape the Moon’s gravity and is thrown up in an arc away from the Moon — all the time reducing speed due to the Moon’s gravitational influence. At some point the Earth’s influence is greater and the spacecraft starts to accelerate, effectively falling toward the Earth.
No matter how gently you plan to leave the Moon, by the time you have fallen all the way home, you’re doing about 25,000MPH. The Apollo command module hits the atmosphere at a very shallow angle (but not too shallow or it would skip right off), digs in and rapidly slows. The forces are incredible — up to 10 G of deceleration, and the heat build up is amazing too. The command module survives because it’s the last, smallest and toughest part of the whole complex and the only part to return. It’s built like a tank. This is all sledge hammer stuff.
The Shuttle would simply vaporize, decelerating at such a rate while generating such heat.
“So, why not fire the Shuttle’s engines to slow it before it hits the Earth’s atmosphere?”
The Shuttle’s OMS engines currently slow it by 200 MPH. That’s it — all fuel spent. The amount of fuel, and the sort of engine, required to slow the Shuttle from 25,000 MPH to a safe speed would stagger the imagination. AND, you’d need to propel all of that extra weight TO the moon in the first place, requiring even more fuel, and even bigger engines…
So, no. Can’t be done.