I would just reassure your daughter that H does love her, he is just really lost right now and probably doesn't love himself very much so he is having trouble showing his love to others.
Then I would tell her, she is old enough to make her own decisions on her relationship with her dad. You will support her in any decision she makes but will not come between or act as a go between for either of them. If she has something to say to him, she says it to him and vice versa...many a counselor will tell you this...it is their relationship to sink or swim with...if you interfere you will be accused of brainwashing and if you don't you still might be accused by H of it but your kids will know otherwise.
Your not his mom, you are your D's mom...be there for her but let her make her way with him...just be sure to reassure her that he does love her...even though it doesn't seem like it right now...
It is hard to see our kids hurt and the first thing we want to do is fix it...and we think that if we tell H he will understand...my H missed his son's first play on stage, missed his first public speaking part, and many other firsts...in the beginning I would send emails, reminders, invitations...then I realized if he wanted to know he would make contact...he was sick and really in all truth it was better for him not to be around...alhtough my son started to pretend he didn't have a dad!
