Have a kids bike that already had 4 to 5 mm difference in chainline. Adding a 13t sprocket to the rear, which won't be "offset" [ in the proper, original direction]... so the chainline will now be 6 to 7 mm from being perfectly straight.

Both sprockets are 1/8" width, but I'm willing to use a grinder on both of them if a 3/32" chain would be best.

To pre-emptively answer some questions...

No, I can't move the front sprocket any farther inward. And I'm fairly certain that I can't move the rear sprocket any farther outward without going back to the original 18t, which I really don't want.

Would a single speed 3/32" chain be better than a multi-speed 3/32" chain? Or should I just stick with the 1/8" chain until i wear it to shreds?

Why aren't there any options available other than the ones you mention?

To answer your question about 3/32" chains, a multi-speed chain will be more flexible as it has to handle offset chainlines. The grinder idea is all sorts of wrong in my opinion.

A chainline being off by 4-5mm will not "wear your chain to shreds" unless your chain tension is insanely tight.

1/8" chain on 3/32 cog and ring. gawd how many times do i have to say this.

This many:

Is that positive or negative?

it's a positive. compensates for approx 2.5mm of misalignment.

Ok great. I run 1/8 chain and cog, but 3/32 ring due to recycling of old parts. Don't know whether I should upgrade the ring to 1/8, but I guess it's no rush then

Taras, I already explained why there's nothing I can do. The front chairing cannot be moved any father inward. The frame doesn't permit anything larger or father in, which is where the rear cog is -- inward. It's a kid's bike. Just the way it is.

As for the rear cog, going from 18t to 13t is moving the challenge father inward. I don't know any way to adjust that besides cutting the spindle nuts in half or something.

I'm trying to find out if sickz' stance remains the same -- 1/8" chain on 3/32" sprockets is better than multi-speed 3/32" chain for 1/4" or more of play.... His suggestion only accounts for about 1/16" off an inch (just over 1.5 mm), considering the bike originally came with 1/8" chain. Would'nt a multi-speed chain suit me better?

3/32 rings with the "too big" 1/8 chain creates some beneficial slop.

*too wide. i wouldnt define it as slop as that suggests the presence of backlash.

Why is the cog not in line with the chainring then? Did you do something to the wheel?

Side slop, not slack.

OP, post a pic of the rear hub. I'm having a really hard time visualizing what you are saying.

dish the wheel, and/or space the hub asymmetrically to compensate.

I'm sorry but It makes no sense to me for anyone to recommend the tiny difference in putting a 1/8" chain on a 3/32" ring to try helping a way-off chainline. 1/8 chains are meant to be stiff & straight while 3/32 or 7-8-9-speed chains are built to be flexible & solve the very problem OP describes. Hell - are none of you here aware of the wide chainline swings you get with 2-3 front rings & a multi-gear freewheel/cassette? A helluva lot more than 1/4".

Get yourself a 3/32" (or multispeed) ring, cog, & (or 9-speed) chain - problem solved...

The original hub was garbage, so I did replace it with a KC hub/wheel... And there's no way I'm about to dish it.

And as far as I could tell, the 13t cogs w/ 3 splines only come in 1/8" width, plus there's a one piece crank with 1/8" chairing that I have no desire to replace... hence, why I said I'll just grind them down.

I think the multi-speed chain is really all I need. Thank you, Sam!