I have two little solder project kits I built awhile ago. An environment noise amplifier and a radio kit. I want to do several things.

One: Reconnect the speaker wire on the radio to output to the amp (has two input mics).

Two: reconnect the headphone 2.5 jack to a 10W speaker. Problem being that the radio has only got a .5W speaker

Three:* Consolidate the circuit power source down to a 12V AC to DC converter.

Four*: Ideas on getting a very clean radio signal? I currently have a ferrite choke on the radio antenna. I also have other ferrite torids and cermaic torids (the doughnut shaped ones) plus one more ferrite choke

* = optional
Schematics (best I could find)
The Radio (Velleman MK118)
Schematic is in the lower right corner of the pdf below
http://www.vellemanusa.com/downloads/0/minikits/manuals/manual_mk118.pdf

The amplifier (Velleman Mk136)
Schematic is in the lower right corner of the pdf below
https://www.vellemanusa.com/downloads/0/minikits/manuals/manual_mk136.pdf

 

Pictures of your velleman kits and circuit diagrams, will get you better results...

 

Yes indeed, you should assume the reader has no idea what a "Velleman kit" is, I have no idea.

If you make me work to even understand what you are asking for, my enthusiasm level becomes rather low.
We all do this mostly for our own pleasure and satisfaction in helping people, but you need to meet us half way.

 

There are some problems with what you want to do. The MK138 is a radio receiver with a built-in amplifer (LM386N.) As you may have discovered, the LM386N is not a very powerful amplifier, but its output is suited to power a small speaker (.5 watt.) The output from the LM386N is monaural, not stereo.

The MK136 is an audio amplifer that is designed to power a set of headphones. The output from the MK136 is stereo, not monaural. Combining the two stereo inputs can be done easily with minimal loss of signal, but the signal level will still be too low to power a 10 watt speaker.

Your best bet would be to find a 10 watt amplifier and connect the output of RV1 on the MK138 to the input of the new amplifier.