Unsure of what your question is meant to discover.

It is actually YOUR vacation, you can do whatever you want within the parameters of time and budget.

If you charter with a USVI company, you could easily spend a week in the USVI and never have a thought about check-in or out. If you want to go to the BVI after that week is over, and you have 2 more weeks, then you would simply go clear in, and not think about it until you needed to leave. Clear out, clear back in to the USVI and have great memories.

If you start in the BVI, then you just do it in reverse. Cruise the BVI as long as you want, check out, go check in to the USVI and stay there until your time is up. No checking out, just go check back in to the BVI.

The only reason it would be a hassle is if you want to go back and forth several times. Again, that would be personal choices, with some necessities required for the choices made.

Absolutely worth seeing as much as you can with 3 weeks. Make a plan and make it happen.