1. Ritualize
I notice a pattern with my kids: going to bed is a ritual, and any deviation is reason enough for them to leave the bed.
2. Slow down in advance
Going to bed after playtime is impossible. So cut screens, playtime, play/listen some quiet music, read books or newspaper (again, no tablet/reader), at least 1h before bed time.
3. Recap the day
Remind your kids of their day, activities and make them aware of the fatigue. Works better when in bed, with mine.
4. Stay with them if they're afraid
Learn why they're afraid, teach them why there's no reason to be afraid. I've had to hang a sock to the door every night for months to scare tigers away :D It just works ^^
Every parent knows the pain and every kid has their own back story and the relationship with the parent(s) is key to finding a way into bed.
Eventually, they will sleep.
In our case, we settled that unless exceptional situations, our kids had to fall asleep in their own bed, because we wanted/needed our intimacy. To get that, I had to stay in my kids' room for as long as 2hrs for months, but didn't let go. Today, going to bed is thankfully not a situation anymore.
I'm not sure this is in any way helpful, but here's my shared experience and learnings. YMMV.
1. make sure they don't fall asleep with something they cannot keep all night (i.e. while you are singing to them, rocking them, sitting next to them or when they are drinking a bottle of milk etc)
2. make sure they understand that even if you leave the room it is just temporarily. Small kids are - for good reasons - very afraid of being forgotten or left alone.
2.1 Using a timer to remember to visit the room regularly and often as they learn to sleep alone can help a lot
2.2. Increase the interval each day. I increased it by two minutes each day.
2.3 If the kids are happy in their bed, continue to visit their room at the scheduled time: you don't want them to think that you forget them if they don't cry.
Using this method I've got my last few kids to enjoy going to bed and sleep better in less than a week fo each of them.
https://www.amazon.com/Bringing-Up-B%C3%A9b%C3%A9-Discovers-...
So for us, when I first started to do this. Each night they get a 'treat' but to get that treat they first need to be ready for bed - eg bedroom ready to sleep in, correctly dressed/ washed etc..
then after the treat they must choose a calming activity - ideally in their bedroom eg reading (nothing that gets their heart rate up) for 30-60mins then they must bush their teeth
It's this point we say time for bed, but we allow them to carry on reading for another 30-60min then it's lights off
if they don't do the activities/ actions after the treat, then we warn them that they'll not get one tomorrow etc. (and really do what you say)
also you may need to flexible on the activities until they get into the swing of it
(The only thing worse than trying to get a child who isn't tired to go to sleep is a child who is too tired to go to sleep.)
Apparently I also still have a sense of humor. Or maybe I don't, because perhaps pretending one doesn't get the joke of doubling down on xkcd silliness is perhaps a joke in itself, which I didn't get.
Also, bedtime trouble usually means not enough outside time and physical activity during the day. Or that the kids want more of the parent's time.
I realize that some parents reach for it every night and this is not something I'm suggesting.