Great topic!
I'm not first generation, but when I went for training for work a couple of years ago, I went to a very "English" place and became interested in my English heritage. Aside from enjoying "afternoon tea", though, there really isn't much I enjoy about it. Most of the traditional English food sounds truly unpalatable. I've never really had the same level of interest in my Swedish/Hungarian side, though.
I do think cultural heritage is very important, though. My son is 50% First Nation, and he has never had access to his cultural heritage. Even if he had any connection with his father, he would not have connection, since his father was part of the 60's scoop. I do believe it's had a significant impact on him, especially when he was going through his adolescent "identity crisis." I also used to work with First Nations people, and have seen first-hand the impact of having Eurocentric settlers try to annihilate First Nation culture. Drastic implications, truly, even all these years later. Just as significant were the residential schools, where removing children from reserves and forcing white culture on them resulted in several generations who have no idea how to parent their children (I'm speaking in very general terms, since it obviously does not apply to all of them).
If you can afford to give your family annual trips back to your country of origin, it might be a great thing for you, to give you a feeling of connection to "home" as well as for your children, to ground them in their cultural and racial roots. I think it would definitely add to their confidence in who they are when they go through their own adolescent "identity crisis."
*End note - my son has had access to a little First Nation culture where we live, although it is not his own band. Some of the practices are common, so I believe it helped.