Hmmm.
Interesting.
My Jewish peeps are very happy to share their traditions with anyone who wants to share with them. Even the more reform ones still hold to traditions for the sake of the children and passing them down.
I'm not sure why your husband feels uncomfortable talking with his father about this. But, I wonder, because you were not raised Jewish, that the new woman in FIL's life isn't quite aware of how important Jewish traditions and family are to you for your son's sake. I use the term "new woman" loosely as it sounds like she's been with your father-in-law for quite a number of years.
I think you should just come out with it and let her know how you feel. It doesn't have to be about holidays specifically, just the Jewish faith in general. She may be incorrectly assuming that "pushing" the Jewish faith could somehow offend you or your own faith and traditions. Let her know that's not the case.
Talk to her woman to woman. I think she will respect you and embrace you when you let her know how important this is to you as a mother.
You say she has a very large family. I'm not sure how large you are talking, however, Jewish women are nurturers. Enlist her help in having a proper seder at your home with everyone welcome. Invite her over to share her favorite matzoh ball soup recipie. Work together in the kitchen and have a nice dinner with her, your father-in-law, husband, and son.
I think if you let her know that you need her and you're really trying to continue to learn and expose your son to the Jewish faith and his heritage as much as possible, things will change for the better.
If you celebrate shabbat at your house and invite her family, surely you will meet some sisters, aunts, cousins. They will embrace you. Your son will get exposure to the men in the family.
Like I said, she may be afraid to trample on your own religion. Let her know she doesn't need to worry about that. Just talk to her yourself.
Best wishes.
P.S. ~ I just read your SWH. I think part of the problem is that you feel it's inappropriate for you to plan certain things because you aren't Jewish. That could be why there is an assumption of uncomfortability for you.
I don't see how it would be inappropriate if you have Jewish members of the family helping you. Like I said, enlist their help. You want your son to learn the preparation and the prayers, etc. If you don't know them, that's okay. You can be taught as your son learns as well. If you don't have it at your house, you can still express the importance of your son being involved.
There could also be an assumption that there's judgement because your father-in-law isn't married to this woman.
I still think you need to talk to this woman and resolve any incorrect assumptions. On both sides. Your father-in-law is your husband's dad and your son's grandfather.
It's worth the communication to keep the ties for your husband and son.
Just my opinion.