This might be abit long, but I don't like the idea of you letting yourelf down before you've started OP.
Firstly, you mention that you have a young family and they need to come first. I get that, I have a 10 month old and a 2 year old. But their dad (my dh) and i are a team when it comes to the kids, if one of us can't pick up the other goes. The kids come first for both of us. What is your kids dad doing, are you together? What kind of support is he going to give you? You need to both be on board, and both very clear and fair about your expectations of each other.
Secondly, you're deciding you've failed before you've even tried. Don't sell yourself short, don't self deprecate, know your value and be prepared to advocate for yourself in every job application. To quote Loreal, you're worth it. Keep that in mind, any interviewer talking to you will be looking for someone who knows what they are doing, and what they are worth. Confidence is key, if you don't have it, fake it til you make it (truly, it works).
On top of that, employers are not even really supposed to ask about your family commitments, let alone base hiring decisions on them these days. And even if they do bring it up, you can use it as a positive, how wonderful it's been to be able to care for your kids, and how exciting it is now to be on the cusp of launching your career, etc etc.
In terms of finding roles to build experience, get your cv off to a few local employment agencies, and give them a call. Ask for advice on how to structure your cv for maximum inpact, and ask them what roles they are currently struggling to fill, as these will tell you where the skills shortages are locally. Don't discount online job seeking websites and linkedin too, I was approached a couple of weeks ago after putting my cv on CV library, and am now in the second round of interviewing for a company that I'd absolutely love to work for, that I didn't even know were hiring. They use a recruiter, and the recruiter found my cv and called me.
On top of the sites mentioned by pp, the open university has a free short course section, where you can take online courses you might be interested in, and coursera.com has a wealth of free online educational courses and resources, to allow you to try out courses and see where your skills and interests lie.
Most of all though, don't sell yourself short, don't talk yourself out of trying, and definitely don't tell an interviewer that you think your young family might put them off. Don't worry about what other people do, who else might be interviewing/applying what they might think of your young family, etc etc. Go for the roles you want, that you think you are capable of, and stand up for yourself as the best possible candidate for that role.