I would prefer to not reference Mass attendance in terms of obligation, as I think that the issue is much wider than simply that.
However, since you ask the question, the answer is that you have a moral obligation to attend Mass when not prevented by circumstances (effectively) out of your control.
That means, in essence, for example, if you are traveling and literally could not attend Mass on Sunday (or the previous evening, Saturday), then you do not have to attend. That extends to being too sick (no obligation) or attending to someone else who is sick and needs your attendance (spouse, child, etc. where you cannot juggle a schedule to attend). It includes camping trips where there is no Mass (one normally seeks permission in this case and it is normally granted).
It does not include not attending because it would offend someone. This is hard, and I can understand that they may not be happy that you have converted, but whether or not you tell them, it would seem from your post that your husband is Catholic and has been for some time (I am reading between the lines) and he has the obligation, and you may be avoiding the full truth of your conversion by telling him that you all attend as a family and will be going with the family.
Frankly, your parents if they do not already know (and it is amazing what parents learn) should be told. You are an adult. There is no doubt that they may be hurt by this, but the truth is the truth. Why not tell them, and while you are at it, make arrangements to go to Mass and attend you father’s service? I am assuming, of course that he is in a Christian denomenation (as opposed to, say, LDS, JW or 7th Day Adventists); but even if he is of those denomenations, it would be certainly a sign of filial love to attend.
That is, as long as you are sure he will not berate you in front of the congregation (stranger things have been known to happen).
The best policy is honesty. I would hope that you would have the occasion to share with him what you have found in the Catholic Church. Getting into a debate doesn’t convert much of anyone, and that is best not a path to tread. But honesty certainly is to be commended.