The short answer is that it varies greatly. You could hop on a bat phone, engage a mob that's up, then kill it and camp all under half an hour ... or you can crawl or farm some plane or TOV for 3+ hours at a time.
Even the "several hours at a time" raids aren't continuous effort though; you should be able to deal with kid interruptions, as long as mom is keeping an eye on them the whole time. And if you have to leave part way through (especially as a caster) it's usually no big deal.
Personally I'd recommend starting with a casual raid guild (
the wiki's guild list groups them). Such guilds will tend to more pre-planned (ie. "honey you've got dinner Wednesday night") and smaller raids, and less long crawls and batphone engagements. Once you've tried a casual guild for a few months you'll have a much better idea of whether you can/should try raiding at a higher level.