If I'm reading the query correctly, you're considering either selling the apartment and investing the net proceeds or re-mortaging to raise funds to invest. Remember that by doing the latter you're gearing up on an existing investment to buy further investments, which themselves are high-risk according to your description. As you mention matching the interest with the rent, I'm assuming that you're looking at an interest-only re-mortgage?
It's high-risk stuff. You need your investment to substantially beat the interest rate over time, after applicable charges and taxes. You also need the value of your apartment to rise. Given your 15 year timeframe, I think these assumptions are reasonable, but not guaranteed.
If you're comfortable with the risks you're taking, I think it makes sense to keep the apartment.