My 5 kids have provided a wide range of responses to my turntables, from mild curiosity to more rigorous physical "investigation." After an expensive stylus was catastrophically removed by one of them at age two, I started covering the dustcover with antique cloths and large chamber pots with ferns. These were a nuisance to remove when playing a record, but deterred the kids from seeing what else would break on that contraption.
Your wife has a valid concern, especially regarding costs. I completely agree with the poster that said vinyl only has to be expensive if you want it to be. You can get something amazingly good for relatively cheap ($300-1000 depending on your luck). BUT...
The problem is that when your El Cheapo rig sounds so good for little, it starts you thinking how much even better it might sound if you upgraded this or that aspect of the vinyl playback chain. While upgrade fever is a core part of the audiogeek hobby in general, it is worst with vinyl, because vinyl is such a multi-headed beast. With sacd or dvd-a, you're only going to be able to upgrade the transport or the processor. With vinyl, you will eventually find yourself in a conversation with your wife that goes something like this:
You: Loving wife, I need to upgrade my $1000 analog set-up to get better sound.
Wife: That's nice, dear. What will it cost?
You: $700 for a USED power supply and speed regulator.
Wife: And then your records will sound great?
You: Er, no. I'll need a better tonearm -- but it's only $900.
Wife: Well, okay. But then it'll all sound okay to you?
You: Heck, no. I'll have to have a new cartridge, won't I? And if I get this one for $900, everyone on the internet says it sounds as good as cartridges costing $2000!
Wife: But then it will be perfect, won't it?
You: Well, almost. There's this phono stage that's supposed to make a night-&-day difference...
Wife: I don't want to even know how much. Surely that's the last bit?
You: Well, those are all just tweaks. I still haven't upgraded the actual turntable, you know the part that spins the records? It's got a motor, a platter, a sub-chassis, a...
And this conversation is just getting started. Wait until her face lights up as you explain to her either A) the great value of spending hundreds of dollars on a machine just to clean & dry your records properly, or B) how much FUN it is to go through arcane manual cleaning rituals.
You also have to ask yourself if you really want all that other great FUN that some people crow about, like scrounging around for decent records that you don't already have. Personally, I kind of like it, although it is tedious, because you see the same old stuff over and over. But for most people with young families, it's simply not a practical use of time, even if you LOVE the sound. Another FUN aspect I like is finally finding an LP that you've been hunting for, and getting it home and playing it, but the sound is NOT staggering. Then you do some research and determine that the particular pressing you found indeed sucks -- you really need to find the one pressed in Holland from May-July 1974 if you want it to sound any good at all. The other nine different pressings of that recording are no good. Silly you. Best to hide that record now before your wife comes in and notices that it doesn't even sound as good as the cd version you already had.
Of course as you rightly point out, this is really no worse than the crap-shoot of finding decent SACD's. But at least you don't have to endlesssly cruise the thrift shops and loser garage sales to find SACD's.
Bottom line: You CAN enjoy vinyl on a limited budget even with kids in the house, but be pragmatic about it. You'll have to make some physical adjustments to protect your fragile turntable, you'll be opening yourself up to a multi-lane upgrade-fever freeway, and much of what others find FUN about vinyl may be a major drag to you (and your family). Like Dirty Harry says, "A man's got to know his limitations."
-Brett