It sounds like their window of tolerance for socialising is quite small and this is likely to do with autism.
First, are they ok at school? Are they masking a lot and therefore might simply need more profound rest, for much longer than you might think is "usual"? My autistic child for example needs up to 2 days in their room alone after a 2 hour social event, just to reset. Maybe they are relieved it's the holidays and the demand of school is lifted but are not expressing this to you, as their inner emotional world might not be easy for them to access, process and communicate?
I guess - are you worried because they arent the same as other NT children or because you feel that they themselves are suffering from not having more connections with other children/fresh air/exercise? And what actually is the nature of the thing they are missing out on? As that might determine the best next step.
Have they had EP reports or do they have regular OT or SLT? Professionals can sometimes determine if they are socially motivated, or motivated by other things, and the strategies you can use to help them extend their comfort zone to get the benefits of connection with other humans, but in ways which do not over stress them but help them practice being with others yet advocating for themselves and making genuine connections.
The fact they need you sounds more frustrating for you than them. It sounds like they each use you as a sort of transitional object- 'when I go outside, mum is there'. It may have become a sort of "rule", then it doesn't even occur to them to do anything differently. I wonder if finding the right thing - and this might be with other adult support more than other children - could help you get a break.
My child was doing no exercise but found it impossible to "just play" with others the social rules were too hard to fathom. They came out with me fine though. So we took them to a weekly club, think rock climbing or circus skills, where there was a clear task and specific tools and an instructor who was almost 121 then they felt ok to do it with lots of breaks. Engaging with other children and doing a modicum of exercise then emerged gradually.
Finally - they are two people and I have lumped them together here. Maybe each of them needs a different strategy for going out more, you might need to do more detailed work finding out what separately motivates each one.