My DCs are grown now but have you thought about going to "The Big Scream" or carer & baby showings at a cinema?
Somewhere like Vue at Ocean Terminal with free parking (babies under 24 months) or in town at somewhere like the Odeon on Lothian Road (buses 1, 2,10,11,15,16, 22, 24, 28, 30, 34 and 35).
They reduce the volume a bit and increase the lighting for a calming environment for you and baby.
The screenings are restricted to 12A so no 18 or 15 certificates. Tickets are priced as normal and your DC's ticket is free.
Or the Filmhouse cinema on Lothian Road in Edinburgh does Carer and Baby Shows.
They usually take place on Mondays at 11am. Screenings are limited to babies under 12 months accompanied by no more than two adults. There are babychanging, bottle-warming and buggy parking facilities and the cafe is great.
You can get parked at Castle Terrace (behind the Usher Hall, Traverse and Lyceum Theatre) and in Semple Street underneath Scottish Widows.