Holdings of United States currency
India: $145 billion.
China: $3 trillion, down from almost $4 trillion.
Gross Domestic Product
India: $3 trillion nominal; $10 trillion Purchasing Power Parity.
China: $14 trillion nominal; $25 trillion PPP.
Bilateral trade deficit with the US
India: $23 billion.
China: $375 billion.
China's economy is bigger
On pretty much every measure, China's economy and its impact on the US is bigger than that of India. While it's true that India has high GDP growth, so does China. As recently as 2013, China had higher GDP growth than India (World Bank). By PPP GDP, China has already passed the US.
It's also worth noting that China acts in a predatory fashion in ways that India does not. For example, China monopolized the market in rare earths. Or the fact that China is the country with which the US has the largest trade deficit.
Beyond all that, India generally acts like an ally while China frequently acts like an enemy. This is not to say that India and the US never disagree or that China and the US never agree. But in general, India cooperates with the US on many levels while China and the US have not. Some of this is the US treating the two differently, but a lot is India and China behaving differently.
The US and India are not fighting over international ocean rights. The US (et. al.) and China are (South China Sea).
While it is possible that India may someday become a threat that is similar to what China does now, it also may stay a friend. And it's not definite that India will pass China. Yes, from 2014 to 2016, India had higher GDP growth than China. But China had higher GDP growth from 2000-2013. We don't know if India's lead is the new normal or just a blip like happened in 1999 or 1989-1990.
The European Union already has a bigger GDP than India, China, and the US. Yet the US does not compete with it as heavily as with China. In fact, the US still participates in a military alliance (the North Atlantic Treaty Organization) with Europe (not quite the same countries as the EU).
Maintaining dominance vs. reining in
It's not clear that the US is trying to maintain dominance or rein in China. In the long run, China would be more dominant if it focused more of its economy on satisfying internal demand. In that sense, the current US trade position is helping China become more dominant. That's somewhat of the opposite of reining it in.
One could view the South China Sea disagreement as an attempt to rein in China, but it may not have that effect. During the Cold War, the competition between the USSR and US led to both sides creating ever improving weapons. Presumably China is responding similarly to the South China Sea, using it to justify higher military budgets. Again, somewhat of the opposite of reining it in.
The US could lower its trade deficit by giving more foreign aid (so long as it gives it in the form of US dollars). This would also tend to increase its influence with the recipients. Instead, it's China that has been giving more foreign aid. That's certainly not maintaining dominance on the US' part.
If the US has as its goal, maintaining dominance or reining in China, it is going about it quite badly. It seems far more like it is trying to pursue narrower goals. For example, it doesn't want to encourage countries to build fake islands so as to expand their sea holdings. That's problematic enough in the South China Sea, but what happens when Mexico or Cuba tries it in the Gulf of Mexico?