Here's a link:
http://www.babycenter.com/0_how-much-sleep-does-your-chil...
Beyond that, sleep pattern changes DO occur. It is common. Not even adults sleep the same all their lives.
Next, its too much change all at one time.
Your Mom NEEDS to put him to nap. A child/baby this age NEEDS to nap.
He NEEDS consistency AND a regular routine. Your Mom should be duplicating HIS nap/sleep schedule, when she is watching him. Otherwise, a child gets discombobulated... and OUT of his/her routine. As you can tell, now.
PLUS, he is teething. My son, like to chew on ice chips... it soothes the gums plus helps the teeth to break through.
It can take time. Or, try Motrin for babies, or Hyland's Teething tabs.
Know that he is normal... this is growing-pains for a baby/child. Its NOT easy for THEM, either.
A child will go through many sleep pattern changes... because they are changing and developing in MANY ways, all at one time.
BUT, keep his pre-sleep/nap routines THE SAME, everyday. Or, it will jar them.
I would not try to change up his sleep/nap times too much, or everyday, or all the time. This will further tweak him and throw his "normal" sleep/nap patterns off.
Its a phase. It WILL go back to normalcy. I know because I have 2 kids, and this happens. And yes, lack of sleep/naps, makes a child/baby mega fussy.... and moody, and hard to console. OVER-TIRED babies & children, actually have a HARDER time to sleep, AND it causes them to wake more.
Give him at least 1/2 hour to WIND-down first, before actually putting him down. That is what I do with both my kids. Regularly. They NEED time to wind-down first... keep everything quiet and dark, give him his milk, read, anything that is calm. Then, "transition" him to sleep and put him down...
Kids/babies need time to 'transition' from one thing to the next.
ALSO, "over-stimulation" can make it hard for a baby/child to wind-down and then to nap/sleep. Any baby/child, ALSO needs time to just hang out, not constantly "playing" otherwise they get too tired and over-stimulated. My son, after about even 2 hours of 'awake/playing' time, would just get tired and start to want to stop. He needed a breather from all that playing. So, I went according to HIS rhythm. I KNEW his patterns of when he was tired and just needed DOWN-time. All babies/kids need that.
Keep trying, but it has to be consistent, and your Mom NEEDS to put him to nap. Napping/sleep ALSO contributes to brain-development & immune system too. So it IS important.
All the best,
Susan