@Thehundredthnamechange
I think your title is very misleading. A friend wanting to come on a honeymoon is outrageous, but this is hardly a honeymoon? It's a road trip with another friend and multiple children attending! It's more like a group holiday! So I think YABU to try to sway the vote with a misleading title! If you don't want Friend 2 to come you just need to tell her, but accept she'll probably be really hurt as another friend is invited and so it's obviously very personal towards her - that you are happy for another friend to join and just don't want HER there, rather than that it's your honeymoon and you want to be alone with your husband.
But it
is their honeymoon - however unconventional the set up.
OP, you sat she has some MH issues that make her hard work? Might it be because of these MH issues that she has invited herself? MH can,and quite often do, make people quite selfish by their very nature.
Personally, I wouldn't use F1 as your reason - it's unfair on her.
I would just be as honest as you can but clear and firect so it's not actually a conversation. Don't apologise because you're not actually.sorrry she can't be there. If you'd wanted her there, you'd have invited her yourself.
I would go with something like.
Hi, Hope all is well. I was caught a bit off guard the other day when you asked if you could join us on our honeymoon. I know I said at the time that it would be nice but actually it is our honeymoon and we'd planned the one that we wanted so it's not going to work for us and I'm going to have to say no on this occasion x
I find that the best approach us to be as honest as possible and as brief as possible.
Someone who lacks self awareness to this degree isn't going to take a hint and will find solutions to any 'reason' you give eg it being full one/child focused/F1 being shy.
It's incredibly rude to invite yourself on someone else's holiday, honeymoon or not; other people going or not. Its not at all rude to say no. If she's going to be a CF, she needs to learn that she's going to be told to back off sometimes...
And then practice saying, "I'll think about it and get back to you."
Bottom line is that you either take her or you tell her she can't come. There is no third option. You don't want her there so make it happen.