> Its not too bad when the kids are at school, but my biggest challenge is to convince my wife that 'I'm working'

If your wife is not respecting your needs around your home workspace, I'd recommend to either start working from a coworking space or rented office, or get an au pair to help with the tasks she's asking you about so that you can work without interruptions.

Thankfully, mine is Russian and treats my work and my role as a provider as sacred, so I get zero friction from her about the time and space I need to do my work.