If we all agree to play to the end of Writing, then there's not much to debate for this set - not much disagreement. It would lead us to T48 with the 2nd city settled, the gold improved and both workers ready to move (1 on the gold tile and the other on the desert tile).
Improving the horse as per Duckweed's suggestion (1 turn only with 1 worker) looks perfect to me.
We will make the 3rd warrior and then 4 turns for 4th worker.
In fact the capital grow to 5 before the city2 grow to 2 at turn61(library finished in same turn). In my micro, pop5 of capital is more important than pop2 of city2. Mainly for the following reasons:
a) capital need to grow to 5 and the library need to be finished asap.The sooner it is finished, the sooner we can take both of the gold mine in capital with library and that's much stronger than a gold mine in city2.
b) if city2 grows to 2 before the capital to 5, then when the capital grows to 5, which tile should you put for the 2nd pop of city2? At that time the cow is not finished.
C) early 2 pop of city2 will face health penalty.
This is an issue for the next turnset. If you haven't, I strongly suggest you run a test with 3 workers before the library. The 4th worker could be started when the capital reaches size 5. Then we could afford a 5th and/or a settler. I haven't run tests past T72 yet but I've seen that starting the Oracle as soon as we have Priesthood is too early.
a) The capital grows to size 5 and finishes the library faster if we delay the 4th worker.
b) The 2nd gold tile can be improved while the capital is still size 4. This means that it could work Cow, Cow, Rice, Gold while the second city works Fish & Gold.
The 2nd city doesn't have a library at the time, that's right. What do we lose ? 2C/turn. What do we gain ? Faster growth (again !!!) because we can work the rice. The capital loses a bit but I'm convinced we gain a lot at the scale of the empire. Also, those hammers in city 2 would be put into the GLH/Library. Far from being worthless.
Finally, 2 gold + 2 cows + horse + rice make 6 improved specials. That's too much for a size 5 capital. So why not share ?
c) Ok, city 2 has -1 food from unhealthiness for a few turns. So the fish becomes a 4F2C tile instead of 5F2C. Still better than no fish at all, don't you agree ?
About the 4th worker, well workers are always not enough. We need workers for city2. We need workers to clean the fallout of city3 and make cottages and build roads. I even found 4 workers not enough, as the fallout.
Cottages... City 3... Maybe we'll do that. Maybe we won't. Right ? Team game ; team decides.
When our 2 warriors will have scouted a bit the surroundings, we will have more info to weight city 3.
And remember we can still build additional workers after completing the library

Most probably, we will not remain stuck at 3 workers forever.
Example. After the 3rd worker, say we focus the capital on food (works forested silk rather than horse and rice rather than forested silk) :
- The capital grows to size 5 and completes the library on T57 (need to lend the gold to city 2 for 1 turn to synch growth and library). If I followed well your plan with 4 workers, on T57 the capital is still size 3 and about to grow to 4. With 4 workers, the capital would grow to size 5 on T63.
That is 6 turns later.
- 2nd gold is improved on T59. That is T57 in your plan. 2 turns earlier, right. That means 4 workers is 14 commerce ahead of 3 workers. Except that... 4 workers completes its library on T60 vs T57 for 3 workers.
I won't provide you elaborate maths but 3 workers doesn't come out behind in terms of beakers. The library is worth 4,75 beakers/turn from T57, then 6,5 beakers/turn from T59.
City 2 reaches size 2 on T61 and, at that point, we can discuss whether to share the gold tile or not (losing 2bpt accross the empire, as stated above).