It seems to me, that you really do care what other people think. If you didn't, would you have mentioned that your family thinks 6 years is too much of a gap ? How long have you known each other ?
If I was in your situation, I'd take your concerns to her. Be honest, and tell her what's on your mind. Communication is a huge part of any relationship, and you may be able to see things more clearly with her thoughts and feelings in mind.
In my opinion, you have to think of the kids too. Should the two of you decide to marry, then what happens if things don't work out ? What happens if you begin to resent the kids for not being your own ? I don't have the full picture here, but I'm just throwing some things out.
It would be wonderful if this did work out, and you were able to become a family, but it seems you have a lot of soul searching to do before you get too involved.
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