For Capital Gains Tax purposes, any appreciation in the value of the property between the date in 1968 that you bought the property with your father and 31 March 1982 is not taxable in any event as CGT was effectively rebased from 6 April 1965 to 1 April 1982. The value of the property on 31 March 1982 is the cost of the property for CGT purposes, at least initually. When your father left you his share of the property in April 1995, its value at that time will be added to your share of the value at 31 March 1982 to arrive at your overall cost for CGT purposes.
The full rules around dependent relative start here
. I won't go over the rules on the home as they have been covered by other experts and you seem to have a good understanding of those in any event. When your parents moved into the property in March 1983, your father was 72 and your mother was 68. They both, therefore, meet the definition of dependent relatives as set out here
. Other criteria for the definition of a dependent relative is here
. Your parents were dependent relatives before 5 April 1988 and the property was bought before that date.
As you will read here
, dependent relative relief can be claimed even if one of the dependent relatives had an interest in the property. You will qualify for dependent relative relief for a percentage of the gain represented by your ownership between the date in April 1983 when your parents moved into the property and April 1995 when your father passed away, in recognition of him being a dependent relative. So, as you and your father owned the property on a 50:50 basis, you will get relief for 50% of 12 years worth of the gain made over 31.5 years of ownership between 1 April 1982 and October 2013.
As I stated earlier in this post, when you acquired your father's share of the property in April 1995, the cost of that share will be the value of it when your father passed away and this will be added to the value of half the property as at 31 March 1982 to arrive at your total cost for CGT purposes.
As for the proportion of the gain covered by the period from April 1995 to June 2013, this is problematical as you did not own all the property as at 5 April 1988 and there is an argument that relief should be restricted to 50% of the gain covered by the period April 1995 to June 2013 as represented by your ownership share at 5 April 1988. However, Section 226 (1) of Taxation of Chargeable Gains Act 1992 here
"Subject to subsection (3) below, this section applies to a gain accruing to an individual so far as attributable to the disposal of, or of an interest in, a dwelling-house or part of a dwelling-house which, on 5th April 1988 or at any earlier time in his period of ownership, was the sole residence of a dependent relative of the individual, provided rent-free and without any other consideration."
There is no mention in the text above that 100% of the property needs to be owned as at 5 April 1988 for 100% dependent relative relief to be due but HMRC may take the view that relief is only due on 50% of the gain. If they do, you should challenge it all the way to a tribunal, if necessary.
If HMRC allow a claim for dependent relative relief for 100% of the gain between April 1995 and June 2013 alongside the 50% claim for the period April 1983 to April 1995, that proportion of the gain for the period June 2013 to the disposal date in October 2013 will be covered by the last 36 months of ownership exemption. The proportion of the gain from April 1982 to April 1983 will be covered by letting relief.
In order to do any calculations, I would need to know the value of the property as at 31 March 1982 and April 1995.
I hope this helps but let me know if you have any further questions.