Put in place a regimented routine and set boundaries that my 3 Yr old will understand. Without mum around he can't act up and play us off one another either. He now knows what to expect and the repercussions if he steps out of the boundaries. I'm quite the fan of the Tonies boxes too. I read him a book and then leave him to pick his own spoken storybooks on his Tonie box whilst I leave him to it to go and do jobs downstairs/feed cats/check little one/make my own dinner/*insert any other excuse to leave him in his room here*. I'll tell him I'll pop back to check on him in X minutes and always make sure I do so he doesn't feel abandoned but lately he's usually nodded off by the first round now anyway. Not having mum about definitely makes it easier though as he'd create more by crying for her, knowing that she'll willfully come running. I found that making his room a more inviting place for him has helped a lot too. He's in to his lego avengers so the bedroom was dutifully decorated as such. It just seemed to do the trick in making him excited about bed time.
/cheapbrag
As for my 1 Yr old, I've carried out the controlled crying routine. It took just 2 nights before he had quite clearly grasped that I wasn't ever far away and that he wasn't being abandoned. I can now lay him straight down with a bottle, say night night and walk out of his room. He usually sleeps right through to morning. This is learnt behaviour, as opposed to teaching him that if he shouts enough he can sleep in my bed.
Both children sometimes still come in to me if they won't settle back off but that's parent life isn't it, you pick your battles. In comparison, our bed time routine used to be non-existent, chaotic and an outright battle where one of us would always give up and end up laying next to child until they drifted off.