Former BUPA employee here and I just wanted to point out that Essential would be a lower level of cover than Plan B. Essential would be more similar to VHI's Plan A or Plan A Options.
If you wanted similar to Plan B (i.e. private room in public hospital, semi private room in private hospital), then you probably should look at Essential Plus.
Please note that I only say this so that you're aware of the difference in hospital cover, I'm not trying to sell their cover or anything. That's also why I won't comment on the service being better or worse, I'm biased!
You can get more info on the Health Insurance Authority's website -
www.hia.ie.
Regarding the tax relief on the premium for your partner and son, assuming you pay this yourself out of your own pocket, the tax relief is given at source (i.e. deducted from the premium so you pay the net balance). This should be the same as what you have at the moment with VHI.