He didn't go to the funeral. Amie tricked him in to taking her to her Nana Deirdre's grave and the funeral just happened to be in progress. Adam recognised the parents from the front page of the paper he read that morning. The girl died from a drug overdose, Adam felt bad about selling the cocaine and cancelled the handover to the drug dealer.
When Ken had a go at him, he changed his mind and rearranged the meeting.
We don't know how Adam knows the woman and neither does the drug dealer who is suspicious of their relationship