You inherited a one-third share of a property worth £130,000 so your base cost was £43,333. You spent £26,000 on improvements and then paid £100,000 for the two-thirds of the property you didn't own. Your cost increased to £169,333.
HMRC may try to claim that the £26,000 you spent should be divided by three as the price you subsequently paid for the other two-thirds would have reflected the increased value of the property as a result of the improvements. Take a look here
for some notes on that. Such a division would increase the gain to £30,000. I would resist such a move by HMRC and claim the full £26,000.
If you sell the property for £180,000, you will make a gain of £10,667. As the annual CGT exemption is £11,100, there would be no CGT to pay assuming you make no further gains in the tax year you dispose of the property.
If you give the property to your son, you will be treated as having sold it to him at its open market value and it will also be a potentially exempt transfer for Inheritance Tax purposes. Should you die within seven years of making such a gift its value will form part of your estate for IHT purposes.
I hope this helps but let me know if you have any further questions.