sock OP's ds2 is 4. He can no more do karting (at least not remotely seriously) than my imaginary 12yo dd2 can take driving lessons.
When OP's ds2 is 10 maybe he'll want to do something expensive, in which case his parents will need to reconsider if money is still an issue - in the meantime it seems perfectly reasonable to allow the eldest to pursue his interest.
If he has sponsorship already then I imagine he's pretty bloody good at it - I know a lot of young karters and none of them have had sponsorship so young.
DP karting is how pretty much all motorsports competitors get into the game. Of course vanishingly few are going to get to be the next Paul Di Resta (although that would be pretty awesome) let alone Lewis Hamilton, but there are many more paths to take than being an F1 driver. Like football or tennis, they all start very, very young.
Lynette :(
OP I absolutely see where chandlery is coming from, but as long as your son's expectations are managed carefully and as long as the others don't lose out too much, go for it. fwiw the younger siblings of the karters I know seem to quite enjoy going along to races and supporting their older siblings. When they don't, then it's time to reassess. Also there are two of you - you don't all have to go along to every event and every training session.
There are also ways of taking part less expensively, albeit with fewer opportunities to get ahead, if you just want to keep his driving ticking over. It's still dear - just more riding lessons dear than re-mortgaging dear, iykwim.