We ran into two issues:
Problem 1: While setting up the tunnel with the ASA, we couldn't get the second IKE phase to agree. We were seeing an error that looked something like "destination host does not match remote host" or some business.
Problem 2: Users at the main site (Site A) couldn't connect to the other two sites (Site B, Site C) when connecting over Sonicwall Global VPN Client.
Cisco and Sonicwall notate subnets differently. If you have a LAN range defined in the Sonicwall but something like 172.16.0.1/21 notated in the Cisco, they will not translate.
The solution is to create a network in the Sonicwall with the matching netmask (172.16.0.1 with the netmask of 255.255.248.0 or applicable netmask).
They will then agree.
Even if you were able to connect before to the other sites, but after setting up the tunnel you can no longer, there is an easy fix to this which I found all over the internet unasnwered, but logging into Sonicwall's site - you get the following KB article:
3) Navigate to VPN Access tab inside the Edit window for the user.
There is one additional step - on the ASA you need to make sure that the VPN subnet has access in NAT0.