Caller,
As has been said, your single entry TV will be invalidated if you leave the country and you'll only get a 15 day visa exempt stamp when you return to Ranong (all land are sea entries are 15 days now. Airport is 30 days).
You can't get a TV in Burma at Kaw Thaung. There's no Thai Embassy or consulate there and your passport will be kept by Burmese Imm so you can't travel overland to Yangon to get one either. So, you're left with 15 days on return to Thailand, that's all.
However, you could go to Imm in HH and get a single re-entry permit for 1,000 THB. It's a quick and painless procedure. If you have one of those, you'll be re-admitted to Thailand until the same permitted to stay stamp as you have on your TV at the moment. You'll not lose or gain any more time here.
It's a while since my wife came with me on a border run, but at the time Thais could get a border pass for 30 THB or so. It's just a scrap of paper that will have the relevant entry and exit stamps on them. Think a passport photo was needed (they can do it on the Thai side). I know she'll have a passport, but if she travels on that (rather than on her ID card) she'll have to pay 10 USD just as you will to enter Burma. Make sure the 10 USD notes are in pristine condition or they'll be refused.
Your entry stamp into Burma will be valid for 13 or 14 days. I can't really remember how long your wife will get, especially if she uses the border pass.
I've never stayed there overnight, but have known plenty of people who have. It's not the most welcoming of places. Virtually nothing to do, you'll be tailed by touts/secret police and I think the town shuts up about 9pm. Shopping, according to my wife, is really no cheaper than Thailand unless you want viagra, horrible cigarettes or gut destroying booze - the Myanmar beer was OK though.
Another alternative would be to go to the Andaman Club and spend a night:
http://www.andamanclub.com/index.html
You'll pay a fair bit more for the crossing, but the hotel's OK (again, I havn't spent the night there) and you can lose all your hard earned cash on the one armed bandits
One of the places to stay on the mainland is the "Honey Bear Hotel". You can't miss it as you arrive. Havn't heard any good reports though. Heaven knows what goes on in there!!
EDIT: You don't need a pre-arranged visa to get into Burma. You'll get the 13-14 days automatically at the border for the 10 USD.