If you rent your home, you’ll need to give notice to your landlord. Depending on what your lease says and what your financial situation is, I’d wait until you have your visa to give notice – that should be sufficient time in most cases. If your lease allows for subletting, you can get the jump on that. Some leases will allow you to buy yourself out with a month or two of rent and a forfeit security deposit. Just keep in mind that some of these things are expensive and some are time consuming.
If you own your home, you’ll have to decide if you want to sell or rent it out. We decided to rent ours and lucked out with finding someone without posting (they really wanted our place and were moving to our town for a new job – they even bought some of our furniture!). But if we hadn’t had someone interested, we would have engaged a property management company to handle things. It costs some money, but in our market, at least for now, our mortgage can be covered by a renter.
If you can’t get the mortgage covered, you might want to consider selling the house. I’ve never sold a home, but I know it can take a lot of time and energy. It might even be easier once you’ve moved out and can repaint / re-carpet and stage your home. If you can find some cheap flights, it might be reasonable to consider the whole family flying over together and then having the partner without a job fly back soon after to sort out the rest of things. Either way, speak to your real estate agent about options.