If we join the Stormcloaks, will we not be allowed into Solitude until we capture it, or will our being in the opposite faction of the town be of no real importance?

That is an excellent question. Hadn't thought of that. Someone else know?

I'd assume you could still come and go as you pleased tbh.

No one would even know you were part of the stormcloaks if you were wearing something other then stormcloak armour.... Unless the chickens snitched on you