I know Orthodox Jews who consider it a very terrible thing for a man to have children with a gentile woman-- not that this means they would support an insincere conversion, they just don’t think a man should ever consider a relationship with a gentile woman.
When my husband was in Iraq, I spent quite a lot of time working with an Orthodox community, first doing some sign language interpreting for them, and then some computer work. I dressed tsnius when I worked with them, and followed all their customs, because after all, they were hosting me, and were very kind to me. They probably knew I wore pants and short sleeves at other times, but I do keep kosher, and at the time I was shomer Shabbes to a much greater degree than I am now (for example, I had timers on my coffee makers and crock pots, and a Shabbes lamp in my bedroom) so I’m pretty familiar with how very observant Orthodox communities work. When I visit my cousin who is Modern Orthodox, I wear my tsnius clothes. My aunt and uncle are very observant, but don’t consider themselves Orthodox. They daven together at home every day (we did as a family when I lived there, albeit, very abbreviated on school days) but my uncle doesn’t lay tfillin, nor wear tzitzis, and my aunt doesn’t cover her hair-- she does dress tsnius for shul, though.
That’s just a little about my background, so people know that I have some personal experience with living Orthodox.
FWIW, a sincere conversion was a simcha, and assisting a person who was in the process of conversion was considered a mitzvah, once it was clear that the person was sincere. There were a couple of women who were in the conversion process when I was hanging out with this one community, and after a number of months, when they had accumulated a lot of Jewish learning, and would often stay for Shabbes (in order to have Shabbes with a family) with the same family I was doing computer work for (they hosted a lot of conferences, which is how they had initially contacted me as a Jewish sign language interpreter). They really cared about these women, and believed in what they were doing, and along with another family, threw a huge party when they completed their conversions. Basically, they treated the women like baal t’shuvah, once they accepted their intent was sincere.
If the OP and his wife want a frumer life, then they need to live that way. If she is interested in a more typical kind of American Judaism, then they should join a Conservative or Reform synagogue (actually, she will have to declare an intent to convert for them to join a Conservative shul, I think, because there is some kind of rule that only Jews can be members of Conservative synagogues). You don’t even have to be Jewish to join a Reform synagogue. I have known of people who joined because they were thinking about conversion, and sometimes took years to make up their minds, and were members for all those years; a few even eventually decided not to convert. I understand that won’t make the OP’s family happy, but it may at least provide a platform for Jewish learning and living for their children, so that if they wish to be Orthodox themselves someday, a beit din may judge that they lived Jewish lives to the best of their ability, if any of them are boys, that their brises were kosher, and may affirm their childhood learning as sufficient, so that they can proceed to mikveh right away. Similar to what happened to my cousin’s wife who was adopted.
