As far as the script goes Harrison had wanted to tell her but could not bring himself to because
a. they had agreed not to discuss it any more
b. every time they did it caused an argument
Harrison had made it clear to Alan that Fallon didn’t feel anything like he did, and Alan realised she did not want to be included in prayers, although he preferred her to be told, but said the prayers were about Harrison’s personal grief.
It was definitely wrong (in my opinion) to include Fallon in the Prayer when no one had sought her agreement. Although the only prayer I recall we actually heard was much more generic.
I see no reason why Harrison should not have had his private prayers with Alan in the church. It was unlikely they would be interrupted (and they were not) and there were a number of ways they could, and possibly did ensure that was the case. It also allowed Harrison to reflect alone in peace afterwards.
I disagree this was wrong and think it unreasonable to describe Harrison’s private prayers with Alan to help him with his grief as such, because he is a person too and obviously seriously grieving and needs help. If Fallon had wanted to deprive Harrison of that, then it is quite controlling, given it was as private as it could be.
Alan totally messed up the first time, but this time it was a private message to Harrison and just “unfortunate” that Fallon saw it as it arrived and read it. I also don’t understand why Alan would have included Fallon in the prayer in the first place given the situation and the fact that he picked the prayers, but if Harrison saw the prayers before hand he should have picked that up. Of course it makes no sense for Allan to have sent them again to Harrison, if he had already seen and agreed them (except as a device for Fallon to find out again).