In order for your wife's tax position to mirror yours insofar as entitlement to main residence relief is concerned, you would have needed to have put the property into joint names when it was your main home. See CG64950 for more information on that. The effect of not doing that is that, whilst you will qualify for relief from CGT on that part of the gain covered by the period you lived in the property and for the last 18 months of ownership, your wife will not unfortunately.
As your mother lived in the property rent free, I cannot see HMRC allowing a claim for letting relief.
YOUR CGT POSITION
Your share of the gain is £19,550 (£89,000 - £39,600 - £700 - £7,000 - £2,600 / 2). The sum of the gain for the period you lived in the property and the gain for the last 18 months of ownership will be exempt from CGT. That accounts for £3,736 (£19.550 / 157 months x 30 months). The remaining gain of £15,814 will be reduced by the annual CGT exemption of £11,000 assuming you have no other gains in 2014/15 leaving you with a net taxable gain of £4,814. As you pay tax at 40% or higher, your CGT will be £1,347.92 (28%).
YOUR WIFE'S CGT POSITION
Your wife's share of the gain is £19,550. The first £11,000 will be tax free due to the annual CGT exemption leaving her with a net taxable gain of £8,550. CGT on that at 18% will be £1,539.00. If it were all taxable at 28%, the CGT would be £2,394.00. If part of the gain takes your wife into the 40% tax band, the CGT will be somewhere between £1,539.00 and £2,394.00.
The calculations assume you did not nmake an election for the flat to be treated as your main home within two years of buying the second. It would have been ineffective in any event as soon as your mother moved into it
Take a look at HS283 for more information on the main residence and CGT.
I hope this helps but let me know if you have any further questions.