To get so stressed about my kids’ car behaviour

Something like this ?

We bought an enormous panda bear and sat it between them. They couldn't see each other round him and totally chilled them out. They could lean on him to sleep. For years Charlie panda went everywhere with us. Putting one in the front created even more arguments.

Mine are the same ages and have just started this nonsense - arguing over who puts their water in the big bottle holder etc. Yesterday my eldest undid his car seat strap for the first time. I'm not a shouter but absolutely lost it. Stopped the car soon as possible. Talked through consequences if there was a car crash), refused to leave until it had gone in. I've told them if it ever happens again, they will
not be going to any fun activities that involve the car again.

This is one of those times you need to properly loose your shit with them. Pull over and let them know in no uncertain terms that you are not putting up with any more crap. No negotiation, no gentle parenting. They need to be a bit scared of your reaction if they ever try it again .

Plan something they really enjoy and travel on a safe route with lots of opportunities to stop and clip them back in. Give them one chance. If they don’t follow the rules you turn around immediately and you go home. Do this every single time until you break this habit. Tell them what will happen before hand. If they get out you buckle them back in and go home. No discussion, no explanation. Don’t engage and do not back down. It’s a bad habit but it can be fixed. You can do this!

Personally , I dont think OP wants any suggestions. She doesnt seem to have done much to control the situation. The kids are 3 and 5 they are little. Country roads have farm gates and houses too. You can pull in, no its not a parking spot like in an urban area but it happens. Its far safer to pull in than keep driving while 2 little kids riot freely inside a moving car on said narrow, bendy roads. Yes I live one some of these narrow roads in the middle of nowhere! I have one who gets travel sick. I have had to pull in absolutely everywhere. You figure it out. OP is asking for advise but replying that it doesnt apply because she is rural, because there is no link... excuses!
If its just sympathy OP wants well yes its hard. Its not fun but it is so very dangerous and you need to be their parent and stop it, regain control in the car. You have been given so many options here but seem very uninterested in them.

Tell them if they are going to not be sensible enough to use adult seat belts (I'm assuming they are both in high back boosters with the adult seat belt?) then you'll get them seats with five point harnesses like babies have (at their ages there should be ones on the market that they fit into!) Then say that if they have to have the baby seats, they won't be able to go in anyone else's car (if they do for playdates etc) as it'll be too tricky to move their baby seats into other cars!

I agree with you. It may also be that OP is driving her children down narrow rural lanes right now, stopping at every pull-in she sees. I'm being optimistic...

It's not a safer option if your eldest can unbuckle him, is it? You need a five point harness

Similarly, one of mine unplugged the harness when we were on the motorway once and I absolutely lost my temper with fear. He never did it again.

Pretend to take them somewhere nice (theme park or something). Then, when they kick off, turn around and go home. Tell them they can go once they learn to behave

A sharp slap does wonders for exactly this situation

That’s a great idea. Try to nip these in the bud early otherwise they’ll be enemies in war for a lifetime.

Well I'm sure the 3 year old at least is in a 5 point harness seat. My 4 years dgc is in a joie spin that faces backward with 5 point harness. Imagine more difficult to escape

Physical violence is never necessary and shows only a parent unable to manage themselves, let alone a child.

My rule when they were young and in that phase was 'I will tell you once to sit down, do your seatbelt up and stop squabbling, then I will pull the car over. If I have to pull over, it's smacked backsides all round and if we're going somewhere fun, not anymore, we're not.'

I only had to wallop them once and cancel plans a couple of times before they learned to behave. Playing up in the car is dangerous to the point we could all be killed if they distract or jostle me at the wrong moment. Absolutely zero tolerance on it did work.