I and my friend, also a rookie rv-er, were surprised at the result count when searching for RV sliding drawer problems. As many of you already know this problem is reported across multiple forums going back years.
Our first step was to try and reduce the drawer momentum from striking and popping the door with padding between drawer and door. But that did not work consistently.
The temporary solution that did work is also the cheapest. Besides keeping the doors closed the only upside was the duct tape color matched our nightcape exterior.

Finally, after brainstorming with my brother, I used a spring-loaded latch on the drawer interior with a t-nut in the compartment wall. They are invisible from the front. They are easily accessible over the top of the drawer front. A couple of nested bolt covers over the latch provide a large, positive point of engagement. A thin self-adhesive bumper on the cabinet frame will protect it from marks if / when you forget to pull the latch spring before closing the drawer. One downside: as indicated in picture below, the top drawer latch should have been mounted on the opposite side to avoid hand / Southco latch interference. It still works for me but may not for others
After install we had the rig on a 300mi round trip camping adventure through some very winding and rough roads. Zero drawer incidents. Tnuts and latches are still secure. I've provided further below a list of steps for anyone that may be interested. Total parts cost was less than $20.
Parts
Spring latches. Search Amazon for "Spring Loaded Left Hand Fixed Security Barrel Bolt Latch"
Small diameter, short screws (don't want penetration of drawer front!)
Tnuts
Rubber bolt covers
Steps
1) Remove drawers from cabinets. Make note of which drawer goes in which slot - they are not interchangeable as a shorter drawer may be on top where the coach body curves. Curiously the slides were different on each side of the coach so the "how" to remove may vary.
2) Place drawer front face down on a flat surface protected by clean soft cloth.
3) I mounted the latches 1/8" from the drawer edge for maximum latch pin extension into the tnut. Mark mounting holes with pencil.
The raised front panels mean I had to use 2 different length screws; a short one nearest the edge and the longer one towards the center. I prefer to have a longer anchor on at least one point.
5) Drill pilot holes carefully. Wrap a piece of tape around the drill bit as a depth stop. I could only find brass screws of the required dimension which can be prone to shearing at the head if pilot holes are not sufficiently deep/wide.
6) Insert screws (make sure they're the right ones if using different lengths!)
7) Reinstall the drawer (be careful not to strike the latch against the frame). Hold the latch closed and test open/close to ensure the drawer is properly seated and fully closing.
8) Drilling hole for tnut. Use a small amount of something (a marker, craft paint, finger nail polish) on the very end of the latch that will leave a mark on the compartment interior. Hold the latch closed, close the drawer fully and carefully release the latch to leave a small mark on the compartment interior.
9) Remove the drawer again.
10) Use an awl or nail to mark the center of the hole.
My drill did not fit inside the compartment. Some of you may have a nifty 90deg head attachment. I don't. One benefit of the mdf compartment wall is that I could easily drill by hand. As in, holding a drill bit in my fingers and spinning it while applying pressure. For any doubters, it took me 20 minutes to drill the three holes in the compartment next to the refrigerator.
11) I started with a small diameter bit periodically checking for plumb and level. I followed with a bit the diameter of the tnut.
12) Blow or vacuum dust out of the hole and dry fit the tnut.
NOTE: I could have used a tnut with a larger diameter hole. This would have given me more latitude with alignment of the tnut and latch pin. I was concerned that corresponding rattling and play would have either dislodged the tnut over time or put too much stress on the small screws. It might also have been a source of rattle. So I went with the snug fit which also required a lot more attention to precise tnut installation.
13) Reinstall the drawer, dry fit the tnut and hold with a finger while closing the drawer and the latch to check fit. I only had one tnut that needed a bit more drill bit attention - my first one where I wasn't paying as close attention to plumb / level of the bit.
14) Remove the drawer (this is the last time; really)
15) I used a loctite construction adhesive for the tnut. Epoxy would also work. If using epoxy make sure the tnut hole is fully cleared after setting the nut. After 12 hours the construction adhesive was still pliable enough for a careful drill bit thru the hold to clear it for the latch pin.
16) After your adhesive/epoxy is fully cured, reinstall the drawer.
17) Add bolt covers to the latch pin if desired. These make it a lot easier to locate and pull the latch pin.
18) Add thin bumpers to the cabinet face where the latch pin would otherwise strike/mark when closing the drawer. These can be trimmed to they don't show when the doors are closed.