Me voy a estirar - I’m gonna lie down
Me voy a la cama - I’m off to bed
Me voy a dormir - I’m off to sleep
Me voy a descansar- I’m going to rest
Voy a tomar una siesta - going for a nap
Acostar los niños - put the kids to bed
Well, my wife yells ‘a dormir!!!’ at the kids when she wants them to stop wrestling and go to bed. When she’s really losing her shit, it becomes ‘a la cama!!!’. But she describes that as a ‘last resort imperative’.
Pienso que eres correcto. There is a word for go to bed but maybe not to sleep and I've forgotten it.