Okay, so, the POD here is the North's 1975 invasion of the South fails. This, due to the US upholding its treaty obligations to provide material support to the RVN's forces. Thus the North's invasion force is obliterated by Army of the Republic of Viet Nam's ground forces and the US's aerial attacks.
This gives the South the time it needs to grow its economy without the constant threat of invasion by the North. By the time the US had withdrawn its military from South Vietnam the North's insurgency there had been shattered. The Tet Offensive was essentially the death knell for organized Communist activities in the South and it only got worse for the Communists after that. So the day to day security threat was reduced to the point of no longer being daily chaos and violence. That, in turn allowed politics and daily life in South Vietnam to start becoming "normal."
Without a Northern invasion in '75 putting an end to all that, the South could begin to grow its economy. That would be the real key to putting an end to the North's threat. A vastly stronger South could then soon enough handle its own security needs without American intervention. The US would still be deeply tied to South Vietnam however. The military bases alone would've been of exceptional value for our strategic presence in the region. This, especially as the leases on the Philippine base leases began to expire and we started handing those over to that country. South Vietnam would benefit enormously from that.
North Vietnam would, in all likelihood, NOT become a puppet state of China. The antipathy between those peoples goes back centuries. And so long as there was some alternative to China, the North would choose it instead. Thus you could expect to see an even greater Soviet presence in the North. The Soviets would not want to lose their basing in that region, the Soviets would want some place to keep the Chinese contained, and the Soviets wouldn't want to see one of their client states implode and fail before the Capitalist onslaught.
So the Soviets would do whatever they could to keep their Communist allies in North Vietnam propped up and functioning despite their having lost yet another army in '75 trying to defeat the South.
In all likelihood, this added expense would probably hasten the demise of the USSR. Perhaps not by much in terms of time but it would be cited as a factor.
Thus the Communists in the North would be in one helluva jam once their patron had fallen. With no Evil Empire™ to keep 'em propped up and with the People's Republic of China's economy booming in the 90s and the Republic of Vietnam's economy having been booming since the 80s, I'd imagine the North would be a pretty impoverished and dreary place indeed.
I can't see the US letting the North alone in all this. There'd have to be espionage and subversion efforts going on constantly to try and bring that regime down.
Perhaps once the wartime leaders had either all died off or gotten so old they could be otherwise put to pasture you might then see some sort of reunion between the North and the South. The constant pressure from China would be a good motivator for both sides to achieve this. For the North it'd mean avoiding coming under Chinese domination. For the South it'd mean avoiding having Chinese troops suddenly manning the DMZ between North and South Vietnam.
When that reunification comes I think they'd find the North to be far more impoverished and desperate than the East Germans were in comparison.