I'm not sure if these are discipline issues, power struggles, scheduling issues, personality traits etc. I'll take any advice from moms who have experience & wisdom to share!
I'd go with the scheduling & the personality & if you are both wanting different things & you want him to comply with your needs without having worked out what his are first & taking them into account then then it would be power struggles too (power struggles tend to need the parent to have by in too) ... as far as being a discipline issue that really depends on how you see it, but IMHO without you understanding his needs & his body clock then he has no chance of working it out himself & not matter if you "punish" him I doubt it will improve. I'm thinking with him getting upset & throwing things with TO he is a child who (like my DS1) needs to understand every step of the way & needs to have some form of involvement in what is happening.
By 3.5yo my youngest had given up naps, but my eldest hadn't, that said he had shorter nights (8.30 to 6.30) because that suited our family esp as DS2 was low sleep needs & still needed a nap but was only doing 10hour nights.
From memory a "textbook" child would sleep around the 12hour mark (in 24hours) at 3yo & it gets about 15mins less every 6months from then on - for a textbook.., for a low sleep needs like my DS2 it would have been about 11hours in 24hours at 3.5yo.
So if you want him in bed at 7.30pm & he say naps for an hour, then wake up would be around 6.15am if he is textbook... earlier if low sleep needs & a bit later if high sleep needs.
As far as enjoyable quite time, a friend of mine started hers by doing 10mins the first few days & building up by 5 mins every few days, so her DD got used to it.
As far as wake up, well that depends on total sleep needs & bedtime & naps.
As far as waking up happy, I think that could be temperament.
First I'd look at what his total sleep needs in 24hour are (add night time plus naps) & then work out what you want his wake up & bedtime to be in an "ideal" world & if you want it say 7-7 then you will likely need to cut out a nap totally unless he is low sleep needs, but the inconsistent wake up makes me think he is more likely on the average to low end, rather than high end.. If you could accept say 7.30 -6.30 then you could have maybe have a 40-60min nap, but even that could mess up bedtime. Another thing I read about was that the "activity" hours from 6am-12 noon impact the sleep from midnight to 6am & the activity from noon to 6pm impact the 6pm - midnight sleep, so having a busy morning can help sleeping in... which kind of works around here as my boys have a heavy sports schedule on a Saturday morning & Sunday's are busy too & Monday's & Tuesdays are the days they are most likely to sleep in.
