I would have the kids stay home - find a sitter or someone from your side of the family to stay with them. Like you said, it's not like it was someone your 3 yo really knew, and at that age, it can be hard for them to understand how they are supposed to behave.
My mother passed away this past summer after a battle with leukemia - she had been in hospice care the last 5 months of her life and her passing was a blessing, so as sad as it was, it wasn't like this huge shock. My daughter had just turned 3 and we had a day and a half of visitation, then a Catholic funeral mass. We had our DD at the funeral home for a few hours on each of the visitation days and many of my mother's friends and our family members enjoyed seeing her there. She really did not seem to notice or ask questions about Nana in the casket. While she did do a fair amount of laughing and running around, she wasn't really disruptive in any way and we did not keep her there all day either. It actually kind of added a little bit of happiness to an otherwise somber occasion - a kind of reminder of how life goes on and we cannot dwell too much on sorrow. When she was not there, many people who came to visit wondered where she was and said they were actually hoping to see her there. We did NOT have her present for the funeral though - I could not expect her to sit still and be perfectly quiet and behave for that amount of time in that kind of setting.
When my father passed away 6 years ago, many of my cousins brought their children who were a little older (6 years up to 9 years old), and they behaved wonderfully, but they were old enough to know what was expected of them and their parents were the type to not allow anything inappropriate. My dad had been in military and I think having the soldiers at the grave site made an impression on them as well, as to how serious it really was.
Bottom line is, it depends on the kids and their ages and how their parents handle them but I would let your 3 year old sit this one out.
And no, your husband should not wear jeans and a hoodie to a funeral - no offense, but that seems really immature and juvenile. It never hurts to wear a suit and tie, or at least some decent dress slacks and a shirt with a collar - this is about showing respect, after all. Even my 16 and 17 year old stepsons had suits, dress shirts and ties for my mom's visitations and funeral.