I have viewed several threads and still not clear on what the options are, very worried

So, my wife is a US Citizen, she lived in the UK for 5 years while we were married on a ILR, we then moved to the US for ten years, before moving back to the UK. We applied for a spouse visa for our return which was granted....
...unfortunately I had no idea there was an expiration date on the Visa, I had thought it was an ILR. Anyway, we went off on holiday and on returning back to the UK, immigration highlighted that this as huge problem and my wife has been an illegal immigrant for five or so months within the UK.
They still let us back into the UK, I would assume as we have a couple of kids and they realized it was a very stupid mistake. However she only has been granted temporary admission for a period of one week, at which point she has been asked to return to the US, they have held her passport.
Question, what are our options? We have two children, both of which are UK citizens, myself who is a UK citizen (same job for 15 years, income circa £50k), married since 2000, she is a housewife.
I cannot return to live in the US due to there immigration requirements.
As I understand, if she were to return to the US and we were to reapply for her VISA as a spouse this would more than likely be declined due to her illegal stay in the UK and deportation.
Last thing I want is for our family to be broken up. I did read somewhere there is an article 8 I believe, from 1998 which states the right to family life. I am assuming I may need to look into this.
Any help would really be appreciated, whats a nightmare this has been
