There's nothing to stop blokes with families applying for any job in the RAF as long as you are within the current limits for each trade (age, quals, nationality, residency, etc) and can prove that they aren't a potential administrative burden (ie not likely to fall behind with the mortgage, no issues that may cause you to disrupt training, missus isn't a nutter, you know the score). Take a mosey down to your local AFCO where the guys will answer any questions you may have. During your period in training, you won't be entitled to families accommodation so you'll only see them at weekends, leave, etc, and you'll have to make provisisions for their accommodation and welfare during that period, but when you are released into the wild, you can have them with you.
Whether it's feasible or not to join, well only you can make that call. Will being a member of the RAF, or any other branch of the forces for that matter, be the best option for your family? Whilst it's good money, subsidised housing, opportunities for travel, etc, will your family cope with you being away every couple of years for 4-6 months at a time on operations? Will your wife be able to find work? - a lot of RAF stations, especially the flying units are in the sticks where work, or certainly work capable of becoming a career for her, isn't always readily available. Will it be a major drama for your kids to move schools every few years? Will you be able to cope financially during your initial training when money isn't brilliant? The good points outweigh the bad (in my opinion anyway) but there's also a bigger picture to look at. Thousands of other people have been faced with the same choices to make as you for years and have gone on to lead successful careers in the RAF in secure family units. Only you can make that decision. As I said, talk to your local AFCO. People in there will be able to provide you in-depth detail on what life is like in the RAF and what your family can expect.
Hope this helps and good luck.