First, congrats on the new baby! And 16 months apart - WOW! :) Mine are 18 months apart.
Anyway, we have the same problem here. My 2 year old is still peeing through most nights. I switched to Huggies Overnights for nighttime and it helps, but hasn't solved the problem. I also don't offer beverages after 5. If he asks, I'll give it to him, but I don't leave sippy cups around. I also will only give him water because he'll drink it slower (he guzzles milk). I just recently started giving him milk in a regular cup for dinner so he'd drink slower (and take less). It has helped with the pure soakers, but he'll still wake up a little wet around the waistband.
I've also tried double diapering him and it didn't work. I have a friend who's daughter does the same thing and she tried the cloth diaper inserts and plastic pants over the diaper. I think she ended up with 2 diaper inserts, a nighttime diaper and plastic pants over them and she'll still have a little moisture at the waistband.
So I say start with the Huggies Overnights and go from there. Its frustrating having to change sheets, jammies, bathe or sponge bath every single morning...especially if you are dealing with a newborn at the same time. Good luck!