Try the charitable route. MIND/ MENCAP sometimes offer inclusive playschemes or befriending schemes so that you could book dc1 in and have time with dc2. Use the DLA to find and pay for appropriate childcare (respite) instead of via ss (there have been some strides in providing specialist sn sitters in some areas - you know it will take a while for dc1 to be comfortable, but over time this is a good exercise for him as well) Carer's assessment (for both dc1 and dh if he is unable to even be alone in the house with dc1) and see if it gets you anywhere. Find activities they can both do. Find out any availability for extended schools schemes in your area for after school clubs etc.
Find out about any support you can get for caring for dh. Try local carer's groups for info. You may find that you can more support for dh than for dc1.
Try looking around for disability screenings at local cinemas / theatres etc.
Contact groups like skinuk and get to meet-ups. Network with the other parents and carers to seek out opportunities you might not be aware of and tips for dealing with your local system. This can lead to all sorts of ideas. (There are always plenty of NT siblings running around).
Get dc2 into clubs and groups in their own right (scouts/guides whatever) as these youth groups will run trips and opportunities to all sorts of places. Sometimes it's ok to encourage them to go without you, even if you really want to be the one going...
Ship in grandma for a week in the summer holidays. (You say no family but not sure if you mean locally or at all. Ours are 3000 miles away lol, so it's occasional)
Ship in Auntie for a week in the summer holidays. (Ditto)
Work on their relationship with dc1 and use the time to pop out with dc2 occasionally. Or to take everyone out and if you need to leave with dc1 (cinema too unsettling, pool too loud) then dc2 can stay and watch the rest of the film. Or do the same with a child carer if no family available.
Find out local parenting groups for sn - often these are a waste of time on one front, but offer good networking on the other.
And last but not least. Be kind to yourself. You are not failing anyone. Cinema and museums are all very well, but no match for a loving family.