16MAR CO0035 LHRIAH 09:20 14:45 or 16MAR CO0005 LHRIAH 10:45 16:10
17MAR CO0443 IAHGUA 11:25 13:18
are available in Economy for the outbound. Nothing without an overnight stop in Houston, and nothing via Newark on your dates.

For the return, the only thing I have found is:
21APR CO1895 RTBIAH 13:00 16:54
22APR CO0404 IAHIAD 07:25 11:15 or 22APR UA0552 IAHIAD 14:14 18:10
22APR UA0948 IADLHR 18:58 07:30+1

The only worry is the connection time in IAD on the return if you take UA552 - just under 50 minutes. But it is a legal connection.

(By the way: IAH = Houston Intercontinental, IAD = Washington Dulles, RTB = Roatan and GUA = Guatemala City, and of course LHR = Heathrow)

You should know that RTB-IAH has a very limited service: a flight on Thursday and Sunday, and two flights on Saturday.

You could also simply buy a ticket: it would be GBP 691 on continental.com and you wouldn't have to overnight in Houston both ways, nor would you have to go through both Houston and Washington on the return. It would then be a simple Roatan-Houston-London. And it could be on the dates you want (well the return would be 17APR instead of 18APR because there are no flights out of Roatan on 18APR.