Upvote:4
There are no restrictions for you to travel to the US at any time, as long as you have a valid visa.
You may be asked for a return ticket from the US by the immigration officer, it doesn't have to be a return ticket from the same itinerary you can buy a separate ticket that departs the US. As long as it shows you leaving from the US it would suffice.
This is not a question asked often, but it has been asked of friends before; especially if this is your first trip.
You can travel to the US and then travel to Ireland. These are two independent journeys, one does not have an impact on the other.
Have a safe trip!