Is 3 hours enough time to transfer between Bangkok airports?

Yikes, this is super tight.

Some info on how to transfer between the airports is here. You don't have time for the bus, so you are probably best off taking a taxi and hope for a driver who doesn't take you on the scenic route, and that the traffic isn't horrible.

You need to get out of the plane, go through immigration, collect your bags, go through customs. Then find a cab and brave traffic. Then go to check in and hope you get to the front of the line before the bag drop cutoff. If your incoming flight is early and you are really lucky, you may be able to make it, but chances are you won't.

If the two flights are not on the same booking, you'd be treated as a no-show and may have to buy an entire new ticket on the spot. I strongly recommend to rebook this.

Things that may help a little: have local cash on hand, check in online for both flights and print boarding passes ahead of time, study the maps of airports, download the apps from the airlines to have up to date info on gates, delays etc.

As already stated, your best bet is probably taking a taxi straight between the airports.

A very useful tip (besides making sure you have Thai baht currency) is to head straight for the elevator in DMK when you arrive, clear immigration and have your luggage. Take the elevator up to the departure level, head towards the entrance/exit and wait for a taxi to come and drop someone off. Most taxis will gladly pick you up instead of having to wait at the arrivals taxi queue!

I have done this two times and it has been very successful - the second time there was literally zero waiting time, I was in a taxi heading to my destination within 5 minutes of grabbing my luggage!

The other time I made the mistake of first heading to the taxi queue, getting a ticket and eating a quick meal while waiting... I gave up after 40 minutes when I realized it would take me at least an hour more, and headed to the departure level entrance where I waited about 2 minutes (there was one other couple who was also waiting for a taxi).

Even so, it will probably be super tight, so you just have to hope for the best regarding delays, luggage, traffic, etc. Make sure to tell the taxi driver to take the tollway/expressway. A useful phrase in Thai might be "leo leo", meaning "hurry" :D

Another option would be to check with the airline you're going with to Samui (I'm guessing Bangkok Airways?) if it is at all possible to reschedule the flight?

At night it would be easier, but during the day, that's possibly the worst-case scenario... Especially if you have check-in luggage. It will take you anywhere from 30 to 60 minutes to pass through Immigration and Customs, and pick up your luggage.

As others have advised, go upstairs to the departure level and take a taxi. It will cost you more, probably. Especially as tourists... In zero traffic conditions, the drive takes 40 minutes (40 to 50 km, depending on the road taken). After lunch, who knows... Hour and a half probably. If it rains (these days, July, it rains every day), don't even bother. Bangkok redefines nightmare when it comes to traffic.

Then if you make it within 2 hours to Suvarnabhumi, you have another long wait. Bangkok Airway has a bunch of counters for all their domestic flights. You and a few hundred happy tourists, and locals, all mixed together. Security is also on the slow side of things. And the gates are far far far away.

If I were you, I'd start looking at rebooking the PG flight to Samui. There are too many unknowns to make any optimistic prediction.