@Hotpants
I have an elder (nt) dd1. Ds1 was diagnosed with adhd and is being assessed for asd currently. I also have dd2 (suspected adhd) and ds2 (nt).
We have been where you are with scouting. Dd1 joined guiding as a rainbow at 5. Dd1 joined beavers at 6. Both have been going for several years now. Dd1 decided when she finished brownies, rather than guides she wanted to go to cubs. Ds1 was due to move up to cubs before she started, but after dd2 and ds2 started beavers (dd1 did a year at rainbows but was hard work and she did not enjoy it).
I had concerns about dd1 joining cubs as she always falls into the role of caring for ds1 when we are not around. I also worried a little about dts starting beavers while ds1 was there and being hard work for the leaders, thus impacting on the leaders impression of the younger children.
But I had to let them try it. There is only one scouting group within reasonable distance and having already done plenty of driving back and forth for rainbows/brownies, I decided it wasn't about to start driving further away just for the sake of a different group and all the extra hassle that would entail.
I spoke to the leaders of cubs and explained my worries, about ds1's needs etc. They could not have been lovelier. Dd1 joined cubs in February, a little after ds1 had joined to give him time to settle in first.
They have been put into separate patrols, they are on opposite sides of the room for flag/howl. The leaders, volunteers, have been fab with both children. They've assigned ds1 a 1:1 of sorts so if there are any problems, dd1 doesn't feel she needs to step in and can stay with her patrol/friends.
Kindly, I think your dd is being unreasonable if this is the only group close to be practical. If there is another group which meets in the same place on a different night, it might be nice for you ds to try there first.
It is always going to be hard when one child is more outgoing and the other has anxieties which affect them in a regular basis. However; others are right when they say her little brother is not likely to be of regular interest to his older sister's peer group.