Part of a cycling club?
If not, don't be afraid to join one and try out the club runs, they will cater for all abilities so I am sure that you will be fine with them.
Anyway, you are allready cycling which is more than alot of people would be doing in your situation. Taking the bull by the horns and just getting on your bike is more or less the best thing for it so congratulations on that one!
Concerning the 95 miles on the first day, you will be more than ready by july

Just set yourself aim, possibly monthly aims such as doing a 15 mile ride by the end of next month? then upping that to 20/25 the month afterwards.
Oh and about that mental barrier you experienced from running, if you are to experience the same thing cycling turn your mind back to what our friend accross the pond, Lance said:
“Pain is temporary. It may last a minute, or an hour, or a day, or a year, but eventually it will subside and something else will take its place. If I quit, however, it lasts forever.”
Congratulations on this feat anyhow

sounds like a brilliant cause. I hope that it goes smoothly for you and that Mrs Merlin doesn't have any more trouble
You will ace this