I have a kalanchoe that happens to need pruning right now too. What I do is wait till temps are warm enough to put it outside so I'm sure it's growing, then I simply cut off any parts that got leggy during it's stay inside during the winter. If they're long you can cut them again to make each section easier to manage. Cut off most of the lower leaves and then you can put the cut off pieces in a jar of water (and some will tell you to put it in a soil mix of some sort but water is easier for me). I dip the stem ends in a rooting hormone first to help them root faster. Some folks root each individual leave but you have a large plant like I do and could end up with a boat load of new kalanchoe plants :-} The mother plant will put out new growth and should fill back out very nicely. I've put a green plastic plant stake right in the center of my kalanchoe and used thin green string to discretely tie it so it doesn't flop over anymore.
Prune every stem back to just above the first set of healthy leaves proximal to roots, then eliminate any stems that spoil the symmetry of the stem arrangement. This is how you maximize the fullness/bushiness of your plant. Don't be timid - I PROMISE you won't hurt your plant. You really should consider bare-rooting/root-pruning/repotting, too. I would prune now & do the repotting around Father's Day.