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Hi. My name is*****'m looking at your question now and will post my answer or ask for more information here in a short while.
There are no reliefs from Capital Gains Tax for the circumstances you describe I'm afraid.
Assuming that you have lived in your current home for the entire period of ownership, you will pay no CGT so long as you sell it within 18 months of moving out. As for the home your mother in law lives in, you will get exemption from CGT for the period (as a proportion of the whole period of ownership) that it is your main home and for the last 18 months of ownership when you aren't living there. The balance of the gain will be subject to CGT, though each of you will get an exemption for the first £11,100 of gains you make in any one tax year.
Another consideration is Inheritance Tax. Whilst you own the property, as your mother in law has lived there rent free since 2001, the start of your actual ownership period, it has effectively been a gift with reservation of benefit and will remain in your mother in law's estate for IHT purposes until seven years have passed after the reservation of benefit ends either by your mother in law moving out or by her paying a market rent to live there.
I hope this clarifies your position but let me know if you have any further questions.
A peppercorn rent isn't a market rent so that would not help the IHT position.
On sale, you might try to claim letting relief which would reduce your CGT liabilities. Take a look at Example 9 in HS283 here.