When repainting architraves and door trims, any paint that can be easily peeled off needs to be removed as it is not bonded to the underlying layers sufficiently. Anything painted on top of a compromised layer will also soon fail.
120 grit sandpaper will remove the old material faster but finishing with 180 grit paper is advised as it will leave fewer visible scratch marks on the timber or paint coating.
On detailed trims, you might find it difficult to remove all of the paint, especially in the corners of the trims. But remember that in order to repaint, you do not need to remove everything, just the damaged and flaking portions.
A good test is if you can feel the edge of the old paint with your finger, then you will notice the transitions after applying additional coats of paint so you will need to keep sanding to minimise them showing.
There is a range of sanding sponges that can assist in getting into tight, hard-to-reach and profiled areas, while an electric sander can help cut your sanding time significantly for the more easily accessible areas. Sanding can generate a great deal of dust, so you might want to consider an Ozito 1250W 12L Stainless Wet And Dry Vacuum to attach to the sander.
Once the weak paint has been sanded off, you'll need to wipe all the sanding dust away and make sure that the trims are all clean.
When you are ready to paint, I suggest priming the surface with Dulux 1Step Prep Primer, Sealer & Undercoat. For the topcoat, I recommend Dulux White Aquanamel High Gloss Enamel Paint.
Here is a link to a handy guide: How to paint like a professional by @Peggers. - EricL
