I just saw Nevada’s post and I think he is correct-replace this thing because if something else goes wrong you will lose sleep over your decision.
To see if there is a problem with the rings of the piston place about a half tablespoon of oil into the cylinder and then see if the compression goes higher. If it does then the rings may have carbon buildup on them and placing some solvent on them may clean them up and get it back to normal pressure. It would be nice to know what the other numbers are. Hopefully the cylinder pressures are within 10 pounds of each other. If the pressure doesn’t change much by adding the oil then suspect a valve problem.
There’s very little chance this will work, but sometimes a compression ring will stick, and you’ll lose compression only in that cylinder. There are magical elixirs that are claimed to unstick stuck rings. This was mentioned by Ray and Tom on The Best of Car Talk show recently in fact. In that case it was for oil control rings. I forget what they said, maybe using kerosene. Or a mixture of kerosene and regular motor oil. And crossing of the fingers.
In your situation OP I can’t actually recommend this. Likely will be a waste of time and money. And even if it works, something else will likely go wrong with the engine soon thereafter. So I think the advice above – either buying another car or replacing the engine – is the commonsense best way to proceed.
I don’t think the mechanics that OP has been going to even know what a wet compression test or leakdown test is
I don't think the mechanics that OP has been going to even know what a wet compression test or leakdown test is
From what I have read, calling them mechanics is a rather large stretch of the imagination.
Why don’t you fix it. You can use it or get alot a more money for it. A leak down test could determine valves or head gasket.
I don’t have the skills to fix it. I am a teacher–not a mechanic & do not know how to do a leak down test. & from the sounds of it neither the valves nor the head gasket is cheap to fix. If I fixed it I would keep it for one of my children. I have already invested in a brand new car for myself. something that I really didn’t want to do. It will put a financial strain on me for a few months but I will survive. I always do. 
“A leak down test could determine valves or head gasket.”
That’s what we’ve ALL been saying
Please reread the whole thread, from beginning to end. In my opinion, it is clear that the mechanics that OP has been going to are utterly incompetent, and don’t know what a wet compression test, much less a leak down test, even is 
Kmull77, I don’t think anyone here is suggesting you fix the car yourself, but are saying have a shop fix it. It seems that if the engine and possibly the CATs were replaced you would have a nice car to drive around in again. You are also short on cash to do the repairs. If you possibly can, you could save the car to be repaired at a later point in time and then pass it on to one of the kids. I assume they are going to need a car sometime in the near future. They may hopefully be in a position where they could help contribute some money to help pay for it. Part of learning responsibility.
While the engine could be fixed you may be ahead of the game to just replace it with a rebuilt engine with ‘0’ mileage, that comes with a warranty. You can get one for around $2,000 dollars. Lets say it costs another 2,500 to 3,000 more to install the engine, new radiator, and a CAT. So for around 5 grand you will have a sound reliable used car for not much cash out of pocket and shouldn’t cost much more in future maintanance. You will know what you have instead of getting something else you have no clue about. Where can you by a used car like that? Even if you had to take out a small loan to help pay the costs I think you would be ahead of the game. If it was me, I would do all I could to keep the car and repair it if someone in the family is going to need one in the near future.