If you're planning on finding an apartment in each place you go (??) than I think you're going to have some trouble finding just that. Apartment rentals are much more common throughout the cities and even still, it might be a bit harder finding them to rent per night. Maybe someone else has some input on this.....?
If you don't mind my asking, why is it you want to rent an apartment specifically? Is it for the privacy and ease of having your own place while traveling with a young one? It will likely be much cheaper to stay at guesthouses than in an apartment so that might be better for your budget.
You're going to find that the most accessible and available option is staying in a guest house or hotel. Internet is available all around SEA but wifi is not very common. You'll have some trouble with accessing internet in Burma depending where you're going to be. In Cambodia, Laos and Thailand there are internet cafes all over...
I'm not overly familiar with wifi hot spots in SEA but I would have to say out of common sense your going to find it much easier to access the internet at internet cafes. I know in Bangkok wifi is spreading but in smaller cities and towns? No dice. In Laos you'll only find wifi in Vientiane and Luang Prabang, not anywhere else. Burma, forget it really. You'd likely have to get connected there as obviously your husband needs access to his laptop to work.
So, long story short, I'd plan on checking out some different accommodation choices and concentrating more on where you can find an internet cafe rather than wifi.
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