Yeah, it's that same old bit where people outside the family, who don't have to live with active alcoholism day-to-day, think someone is wonderful. Because somehow...the alcoholic is able to maintain some sort of facade. Those nearest to him/her have to deal with the broken promises, the no-shows, the verbal and mental abuse, the manipulating and gaslighting.
Your daughter does get to love her Dad...and as she becomes an adult, she will be able to incorporate all that she knows (good, bad, and ugly) into the whole person that he was and maybe still love him with all his flaws. There is always that moment--even with great parents--when a child reaches adulthood and understands that their parents aren't perfect human beings. Your dear daughter just learned quite a bit, quite a bit earlier than she should have had to learn
I'm sure the funeral, overall, was very hard for you for many reasons. Process as you need to do - we are always here!