Star Alliance - STO-SIN-CHI-STO with kids, RTW advice needed?

I'm travelling STO-SIN-CHI-STO this summer with a child and an infant.
Because of the kids, I want to minimize airtime, but also the number of stopovers. Avoiding very long routes/detours is also a good thing.

I'm trying to figure out which tickets we should get to achive above without paying too much.

When comparing *A, OW and ST, I came to the conclusion that *A would offer the least number of stopovers, since none of the others have direct flights CHI-STO. On the other hand, OW offers slightly shorter airtime on STO-SIN (with AY), and the added advantage of flying out from BMA instead of ARN.

I was looking at the different RTW fares, but realized an adult RTW ticket with *A as above is around 27500 SEK or $4100 (adding in NRT as an additional segment to fulfil the requirements).

I've read about "mini RTW" but I'm not sure it's applicable in my case. Is it just the same as buying a single one-way ticket + an open jaw?

Would it make sense to get one-way tickets STO-SIN with AY, and the open jaw SIN-CHI/CHI-STO with maybe UA? If so, should I buy the UA open jaw tix from a travel agent in SIN, or maybe it doesn't matter if I buy them from any other online vendor based elsewhere?

Or is there some kind of multi-city deal with *A besides RTW that might be cheaper?

Thanks for any advice you might have!

You are wasting a lot of the possiblities of a RTW - and they are usually not a good deal in economy anyway.
One way tickets are usually more expensive than round trips, especially in economy.
Did you consider doing this as two RTs STO-SIN-STO and then STO-ORD-STO?
Another option is Turkish. You could combine STO-IST with IST-SIN and IST-ORD? Depending on the dates you should be able to do this for less than 3000 $

Thanks for your fast reply.
Yes, I was considering two separate RTs, but it would probably mean more airtime/segments for the kids. But maybe it's still a cheaper solution?

Turkish sounds like a feasible solution. Full itinerary would then be STO-IST-SIN-IST-ORD-IST-STO? Would I buy this ticket as a multi-city with them?