I have found replacement handbrake shoes take a bit longer to bed in than the pads, and the handbrake isn't as efficient as you would expect until bedded in. I presume this is because the shoes only contact the inside of the drum when the handbrake is applied, whereas the pads contact the discs every time the brakes are applied and bed in quicker. With new shoes, I have driven slowly on a quiet piece of road gently applying the handbrake which helps to bed the shoes to get a reasonable handbrake from the off.
Make sure the shoes are adjusted equally or the handbrake will pull unevenly. I would also check the return springs on the backplate as they corrode and become weak. The locating hole in the backplate can also corrode.
You will have to unfasten the caliper to get the disc off; just be careful with the metal brake pipe when unclipping it from the swinging arm, and support the caliper so that the pipe isn't under tension whilst doing the job.
Don't forget that if your rear discs are vented, the retaining pins are longer than on solid discs, and not every motor factors will supply the correct ones.
It's not a difficult job - but the right tools always help!