The uncertainty established by the new Trump administration has brought the future of the dollar and currency in general in question more seriously than it has been in many years. For good or evil, the Trump administration will enact a great many changes especially given its current influence over congress and the floundering GOP.
We must look at two possible scenarios over the next couple of years to get an idea of where the dollar is going:
1) US involvement in international conflict
As long as the dollar is tied to oil, international conflict will continue to play a major role in its value. Given the appointment of a major oil mogul, Rex Tillerson, as head of the State Department we can assume that this dynamic will continue. The main fear is that conflict, as it has done in the past, could cause a major drop in oil prices. However, given that the US now produces of 70% of its own oil and continues to ramp up production, and has extensive reserves this may not be the case.
In theory if a conflict in the middle east- say with Iran, Saudi Arabia, or involving both were to shut down significant supply to the market the value of oil would skyrocket. Rather than acting as a drain to the US economy it would give it a major trade advantage, lowering production and transportation costs compared to those in the EU. This would also benefit Russia, who would be able to make more money per barrel. China would also benefit as both the US and Russia are the major consumer markets and boosts in their currency will be reflected positively in the Renminbi as well.
When a conflict benefits all the permanent members of the UN Security council, take notice!
The exit of the United Kingdom from the European Union will have far reaching economic implications. In all likely hood, the Pound will be on par with the Dollar in the not too distant future. The main question is will it continue to drop after that point or will it rally? I suspect we will see an extended period near Dollar equivalency followed a slight rise as long as the UK deals with its labor issues. England especially is struggling with a similar loss of middle class jobs due to technology. These jobs are not coming back, but creative legislation can help mitigate the economic pain of the former middle classes in both counties. If this occurs for England the Pound has a bright future.
Luckily for the US I do not think fluctuations in the Pound hold significant risk for the future of the Dollar. EU stability, however, is a different matter altogether. Should Brexit and other factors impacting the EU lead to further loss of member countries and more instability, especially in France and further East, this could certainly bring the Dollar down.