The exact dating website for what you want seems to be (the infamous Ashley Madison)-
https://www.ashleymadison.com/app/m/login.p
However, I didn't like it, but a few others appeared fine with it. Maybe I need to redo my profile. Tested it out a few months ago and still have a lot of points left to use. Website, at least their Japanese version, gave off a very scammish feel. It doesn't work like most dating websites. You have to buy points, and they find ways to make them disappear quick. It also appeared to be very infiltrated by pros. Many of the women who would e-mailed me outside the site were p4p that wanted to negotiate price or cam models trying to direct me to their website. It pissed me off and I complained to Ashley Madison staff and they banned some of those accounts. Still, left a bad impression. However, others say they found success with the website, so might be worth a try. I will look into them again, but doing well with other websites and sarging ("street" PUA), that not in a hurry.
Other websites like JapanCupid, OkCupid, PlentyOfFish, Match, Tinder, or language websites... Let you search by age. Skout (smartphone app) searches by distance and you select the profile (thus her age) manually. Those have been decently successful for me. However my search age is wide, 18 to 40, not specific to 35+.
Women who might be married appear not to say so on our dates. I don't push it in questions... Why? Technically, under Japanese law (which is a bit odd), her spouse can sue you for cheating with his wife. The slight loophole, that you can try to use in court, is if the wife never told you she was married or lied about it. So, for me, if they are married than I initially don't want to know and especially if we are just going to hotels and happening bars. However, if I'm thinking to bring them to my apartment, I ASK. If they tell me they are married, then they can't come to my place. And, if we continue a sexual relationship, it's happening bars or swinger hotel parties only. This is another slightly higher level of protection. She can be having swinger sex with other women and men in the club or parties. A Japanese wife would almost always not want it revealed that she goes to happening bars or swinger parties and will often work EXTRA HARD to protect this secret. Plus, Japanese wives that crave sexual release, will often be very appreciative of a swinger guy that converts her to the lifestyle and guides her.
When it comes to sarging (PUA at coffee shops, video/CD rental stores, trains, clubs...), I tend to go for 20 something women and do well with this age range. There isn't a problem for older guys to date younger women in Japan, Korea, Thailand, or China. Probably applies to most Asian countries. A guy can be 41 (stay in shape) and with a 21 year old, and nobody cares or raises an eyebrow. Many younger Asian women don't mind, and see older guys as a benefit in terms of experience, financial stability, maturity, mentoring, etc...
I've picked up 30+ and 40+ women, to a lesser extent, when sarging (sometimes because they looked younger than their true age) and they usually hide that they are married. Again, I don't press for such information at first. It's on her to tell me or stop our conversation.
If you only want 35+ and married, if sarging about doing PUA, you would have to focus very hard. Just go looking for rings on women's fingers. That's bypass talking to all other available women or even women showing you interest, until you find that specific type. I find that hard to do. Who you will encounter and success tend to be random or unpredictable. And I'm not throwing away an interested hot 25 year old, for no reason. Websites would be more practical for locking into a specific type of woman. Maybe other users can list other dating websites married Japanese women use or specific hangouts older married women like.