It sounds to me like you and your husband need to talk about some of these feelings. If he is indeed rolling his eyes, then he isn't standing by his promise to back you up on faith based decisions. If you are feeling ridiculed, that can't be good for the trust you feel or for the example you both are setting for your children.
Could you bring this up with your H and explain how you feel and then make it safe for honest responses from him? Once you validate each other, then you can move to negotiating some solution that may work better for the two of you. If he disagrees with what is happening, perhaps he could think of a kinder way of addressing it.
I think I agree with Racheldrew in that FHE's can be recreational and inclusive activities. But I think we shouldn't forget that the teaching of the gospel to children is to be done in the home first. We shouldn't rely on church only to make sure our kids have a solid understanding.
I don't know exactly what to say about how you are feeling about the church. Sounds like you are slipping into some isolation. What about talking to the RS pres? This isn't a worthiness issue. The bishop isn't needed. Perhaps the RS pres could adjust your callings so that you were more involved or so that social opportunities could be opened up for you. It is hard to be a part member family. I think you need some extra support. Are there other partmember families in your area? Maybe you need to make a friend with someone in the same boat.
And you know, maybe this is just another one of those spiritual down times for you. Your spiritual tank is low and you just need a good refill. Put your energies into the filling, instead of the worrying because you aren't full.
