Let me get to the conclusion up front - if you have kids under two, I wouldn't go. Granted, any vacation with kids under two is bound to be stressful, but even Carnival's much-touted kids program isn't much help here. But let's start at the beginning.
The check-in process is pretty smooth (even though the security screeners restrict more items than what is listed on Carnival's website). The rooms are what you would expect - standard 185sqft without anything fancy. The "individual temperature control" is a little dial to increase or decrease the cold air flow. The flat-screen TV is using an analog signal (and only on suites can you use your own input devices, and even there only with RCAs). The bathrooms show the most indications of the ship's age (it's from 1996, with an upgrade in 2009), and there are random bad design decisions, like the light switch for the bathroom being outside of it, making it a prime toy for little kids. Turns out that taking showers in the dark is pretty cool though. Hint for first-timers: Come early. There's a lot to do on the ship early on, so you'll miss a good chunk if you arrive later during the embarkation process.
There's only one 110V and one 220V outlet in a room, so bring a power surge. However, certain power surges (they don't say which ones) will be confiscated. Try something small - I brought a compact one with two extra outlets and two USB charging ports, and they were fine.
After the drawn-out safety briefing there's an orientation for the kids program, Camp Carnival. Once you're done with that, you'll want to eat - and realize that many of the buffets have already closed down. Nice timing there, Carnival. Still, you'll be able to get some hot dogs on already-stale bread, and there are still plenty of genuinely tasty desserts, so you won't be hungry. There's also a 24-hour pizza and late-night sandwich stand.
Drinkswise, there's tons of juices in the mornings (including a great orange-guava-passion fruit mix), and lemonade and hot chocolate all day, all free. But you have to pay for soda. Not much of a problem for me, I like to keep my soda consumption down. In fact, I applaud this choice, it just seems like an odd decision from a financial standpoint. Especially because the free options are quite good, the lemonade even has lots of pulp in it.
After eating, you'll probably want to get your kid into Camp Carnival. The check-in process is tedious, especially when you're coming at a hotspot time - each child is processed one by one, and most parents apparently have reading comprehension problems and need to be explained what had been laid out before during the orientation, so it can easily take 5-10 minutes to drop your child off, even though it's a matter of showing your "Sign & Sail" card and have the child pick up the name tag. Same with pick-up.
Now for kids under 2 - they can't go to the kids club, even if they're just a couple of weeks shy of being 2. There is no child care option for them whatsoever, except for Night Owls after 10pm. Kind of nice, but guess when the gym closes? That's right, at 10pm! Same with many other amenities, like the pool. And since diapers are not allowed in any of the water-related offerings, you won't be able to experience them, period.
There's also under-2 service at assorted other odd hours (like on one port day from 10am to noon), but those are essentially useless.
Also, child care after 10pm is no longer complimentary. It's reasonably priced, but at the same time, it's not like a true babysitting service - if your child starts crying, they'll simply call you and ask you to pick the little one up.
Even during daytime, the camp is closed for lunch and dinner, so you'll have to pick your kid up every so often, the exception being on port days, where they give your kids lunch and dinner if you tell them up front that you'll be on the shore. This is particularly infuriating when you also have an under-2 child to juggle around - you'll have one parent enjoy themself while the other one takes care of the little one, picks up the big one from camp, etc.
The two options for dining on the Inspiration are the buffets on the Lido deck, and the MDR. For the MDR, you have three options - early seating, late seating, or open table. The latter sounds the most enticing for parents - you come anytime between 5:45 and 9:30, which is great to work around odd napping schedules. The problem here of course is that you're on the bottom of the food chain as far as priority goes.
You'll stand in line to get a buzzer. Then you'll wait an unspecified time ("can't tell you how long it takes, depends on the guests") until the buzzer goes off. Then - my favorite - you stand in line to present your buzzer and be seated. The funniest part about this line is that there'll be plenty of people trying to brush past you with blinking buzzers, and you'll have to explain to at least five people that this is the line for people with ready buzzers.
Dinner itself is decent though - there is a good deal of choice (half of the entrees available every day, half on a per-day basis) with a reasonable kids menu, and the staff is generally very friendly. Pretty much everybody on the ship seems to make a point to either already know or remember your name. The food itself is not bad - the MDR food isn't exactly high-end fine dining, but still quite good. The food on the Lido deck varies in quality.
The Inspiration heads to Catalina (on the 4-day cruises only) and to Ensenada. Catalina offers enough to do during the relatively short stay, and the biggest advice for Ensenada is not to take the Bufadora or horseback excursions offered by Carnival. You can book the same ones on-site for much cheaper - get a shuttle to downtown ($3 for a return ticket for adults), and they'll drop you off at a ticket counter where you can get the excursion for half of what Carnival wants (plus - they're much more lenient about not paying for kids). We paid $15 for a trip to the blowhole for each person 5 and up - Carnival wants $28 (for kids 4 and up). Also important - be sure to bring cash to Mexico.
We chose the blowhole because it seemed like the least crappy activity offered - keep in mind that Ensenada is not a particularly exciting location, its prime interest for cruise lines is its proximity to the ports in Southern California, so I lowered my expectations to a minimum. With that, it was surprisingly good - we hit the blowhole at a very good tide, so the water shot up in the air very high; it was off-season, so it was not packed, and the peddlers were most certainly not aggressive, even though virtually every review claimed that. I guess people are a bit sheltered. To get to the blowhole, you have to walk through a large flea market, and every thirty seconds, someone will try to sell you something, like pharmaceuticals and knock-off watches and handbags (one of them offered to "rip you off for less!"). But they're not in your face, and if you say "no thanks" once, they'll get you go.
To come back full circle - I wouldn't go again with kids under 2. It's like being in a candy store when you're diabetic. If it wasn't for that, it's a great entry-level cruise. The staff was great throughout, and I have to mention their fondness of addressing you by name again. I'm sure it's a company-mandated policy, but it works. I was randomly walking through the buffet area to get somewhere, and a waiter we only met once before greeted my son by name in passing. It just adds a nice personal touch to the trip.
Of course, the Inspiration is not like a brand new 3500-passenger dreamliner with dozens of restaurants and multiple fancy swimming pools (this one has one hot tub, a plain rectangular 5 foot deep swimming pool and three water slides), but this was our very first cruise, so we got to see how this whole cruising thing is. And we liked it. We'll do it again.
Final tip: Since the vessel is spending most of the time traveling South, I would recommend a cabin on the port side (=even cabin numbers). There'll be more to see out of the window. Also, since you are more likely to hit the buffet with kids, stick with a cabin in the aft so you can get there quickly without having to walk through the entire ship.
Here are some of the pictures I took. The 360 degree panoramas are typically pretty bad because my son just wouldn't sit still while I held him.