Fathers will wear black suits; groom is wearing a tuxedo;I suppose they've decided to follow a daytime semi-formal attire. Your husband is expected to wear a white or silver tie.
How about trying to find out if the bride's mother is wearing "a kimono"? If so, a long dress would quite suit that. The hours sound okay to me as well. But if this is going to be an occasion where the bride's mother is wearing a knee-high dress or suit, of course you'd want to wear something similar.
I understand that these things are very important to you. I'm sure your son simply doesn't want you to worry about anything, but tell him that you want to look good in front of the guests and that you need to know about all these things, otherwise you'd be more worried. I'm sure the bride's mother would most understand that. Especially, it's a normal thing to check on each other's attire so that the whole banquette would look good for everyone.
From a quick internet search, the following website of a popular wedding information company is designed for the parents.
http://zexy.net/contents/oya/Fathers' attire (left-bottom is black suit)
http://zexy.net/contents/oya/dress/kisopapa.htmlMothers' attire (bottom two are supposed to match fathers in black suits attire)
http://zexy.net/contents/oya/dress/kisomama.htmlActual examples of semi-formal
http://zexy.net/contents/oya/dress/semiformal.htmlAs for the "meet the families" dinner, ask your son what he is wearing and adjust yourselves to that. Typically, it could be anything from T-shirts-and-jeans to semi-formal suits. Asking which restaurant they've booked might help too. You could check the restaurant's website and find out the atmosphere.
By the way, I'm a Japanese resident, a working mother in my 50s and whenever I can't decide between jeans and semi-formal, I try to wear a nice jacket and a daytime dress that may look a bit casual without the jacket. Your husband could perhaps bring along any kind of tie so that he could decide whether to wear that or not on the spot. But all in all, wearing something similar to your son solves the problem.
As for gifts to the family, just do whatever is typically done in your hometown. The bride and groom seems independant and if your son says you needn't worry about anything, then I suppose there are no conservative rules among her family.
I suppose something popular in your hometown would be typically appreciated, but in these days where you can buy any foreign item on the internet, I simply try to give whatever
I like when I'm gifting. It would be a good excuse too to say, "I'm not sure if this would suit your taste, but it's one of our favorites."
Keep in mind, however, that a lot of people in Japan don't use cars to go to dinner, so anything bulk should be sent on another occasion (so giving only light things is what's typically done in the cities). On a related note, no one is expected to bring along item gifts on the day of the wedding, as guests and hosts have too many things to take home (typically, cakes and gifts would be arranged for all guests and hosts to take home).
As for payments, if the young couple is arranging the dinner, I'm sure that's all been taken care of by them. If you decide to move on to other places for an extra drink or tea, I suppose it's universal for some fathers to prefer to pay or to take turns in paying.
Note that most places in Japan don't do "table check." In other words, you don't call the waiter to the table for the bill, but upon leaving, you all go to the cashier to do the payment, be it cash or card. A smart way to pay for everyone is to go to the mens room towards the end of the meeting and, on his way back to the table, to discreatly ask the staff and do the payment. But again, I'm sure the dinner is all being taken care of. I'm just talking about other occasions, if any.
I hope you get everything organized in your mind so that you could just sit back and relax once you've left for Japan. For most of your stay, you are the guests!