Do not worry about being "behind the curve" or "not finding your niche"--some nurses hit the jackpot straight out of the gate... but honestly, I think most of us end up doing several different specialties before finding one that "clicks."
I have been a hospital nurse for 5 years; started out in tele, did travel nursing, and went on to ICU eventually. I am probably happiest in ICU, but it took awhile to find a unit that was a good "fit" for me--both from a specialty point-of-view and from an "environment/culture perspective" (there are some units that are better than others!)
As to scheduling and 12s: I do not know if you have been offered a day or night position, but typically, you will orient during days, and then rotate to nights afterward--and it can take a long time (a year or more) to rotate back to days. Have you worked full time night shift before? I could not tolerate nocs; they made me physically ill, and I had no choice for awhile but to work them. I cannot imagine working nights in the state I was in, and raising a family. People do it, but I don't recommend it. Some people love night shift, but you have to know yourself, and your circadian rhythms, and realize that even people that work night shift and wouldn't work any other shift generally had a "breaking in" period--some up to six months. That's a long time to go sleep deprived ;-).
Also, please realize your schedule "will not be your own" during orientation, and regardless of which shift you are assigned afterward, scheduling managers vary on their policies for requested scheduling patterns, and as "low-man on the totem pole"--your requests may not be heeded. You also have to think about accrual of sick time, vacation time, etc. It takes quite awhile for that to add up, and as you say, you need to worry not only about your health, but your children's, too. Take into consideration also how you feel about working holidays--how important is it for you to celebrate with your family? Often, you have very little choice in what holidays you work... and you will work some of them, and sometimes not the ones you'd choose.
In other words, yes, you may be lucky and get a shift and scheduling pattern that is compatible with your family life--but this is probably not going to happen your first year in hospital nursing. In my experience, as junior staff, you have the least control over your schedule.
If you do not need benefits, I would seriously consider why you wish to pursue hospital nursing at this point in your career. While I can understand your eagerness to learn acute care skills, you are just starting out, and trust me, there will be time and opportunity for you to become a hospital nurse. The home health care job sounds like it has the perfect amount of flexibility you require to maintain your family life. Family is important!
Hospital nursing, as others have attested to, is extremely difficult, stressful, anxiety-provoking, exhausting, and being a new grad exponentially raises the ante on all of those emotions. The practical reality of hospital nursing is that it will take at least 6 months for your to feel somewhat comfortable in your new role, and at least a year for you to feel proficient.
I am not trying to discourage you from becoming a hospital nurse, if that is what you wish to do; only suggest that this is not a decision to be taken lightly, and in today's employment economy, it might be more prudent to hold off on the job offer and commit at a later date rather than "jump in" and have to quit because it isn't working for you or your family. I also think you should not worry about "being too old" to start a hospital nursing career if you wait a couple years--there are plenty of people of all ages who come to the profession and do just fine.
Follow your heart and do what seems best for you; my suggestions are only that... just points I've gleaned from my own personal experience in nursing that I think might be relevant to your situation.
Let us know what you decide, and congratulations on your new career!