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You have done well with that first attempt. The original is quite badly faded but I suspect it was also over exposed due to using flash -- there is more detail in the background than in the faces.
Because of this, you will never get a fantastic result -- but it is possible to make the faces a bit more recognisable using the tone curve:
I started with your second picture and used a mask to apply the curve only to the left side of the image so you can compare the results. It does unfortunately boost the grain as well as the facial features. To get the best result you need to experiment with the levels at several points of the curve to identify the points that represent the features, to increase the contrast at that level and reduce the contrast at less important levels to avoid the background looking too dark and dingy.
I have not tried, but I think you should also try applying the tone curve before applying your lab values.
Another thing you could try is to make a copy of the photo and use the cutout lab to isolate just the people. You can then apply the tone curve separately to the people and the background.
When you have the best result, you could try to reduce the grain with some of the options in effects > blur
Finally, you can remove the specks by careful use of the clone tool copying from other areas of the photo. Hint: if you can't find an area of exactly the right colour, set a feather and use 50% transparency and then copy from a clean area of the same colour, clicking in slightly different places 2 or 3 times on the spec until it disappears -- the transparency, feather and the jittered clicks will much reduce the difference in colour.
This is the best I've been able to get.
I started with the original. Made a duplicate of the background as a new layer. Used the Contrast Enhancement tool to up the contrast to the maximum, then made that layer 50% transparent and used the Multiply merge mode. Then I combined the layers and used the BD Grey Balance plugin to tweak the colours.
It's maybe managed to pull out a tiny bit more detail than your attempt, but there's not going to be a lot more to get from that original.
HDR might be a way to go too, (sadly and/or intentionally omitted from PhotoPaint?) This was done with NIK (Google)