Ugh.
You sound like my exh 6 years ago.
Often mithering for sex and if he hadn’t had it in a couple of weeks would start pawing at me in the middle of the day in front of our young kids.
Like you he’d go on about how fantastic I was and a great mum to our amazing kids but it was all performative. I had to do everything, housework, most of the parenting, and in the end bring in most of the income. Some examples:
Left the house for 45 minutes to get a flu jab and he moaned I was gone too long.
Text me when I was WFH (he wasn’t working) asking me to watch the kids while he made dinner.
Ask for lists of what needed doing in the house then didn’t do any of it because “it looked fine”.
Told me to take up a hobby but didn’t like it when I took up running because it took me away from the kids.
Asked me once during the pandemic why I couldn’t just look after the kids all day and work when they’re in bed, so he wouldn’t have to do the parenting on his own. I was never allowed any time to myself without being made to feel guilty.
It was just unattractive and in the end I just felt like I had a third child to look after rather than an equal partner.
My suggestions for you:
Buy presents that aren’t lingerie or anything to do with sex. Buy things for her that are related to her interests and hobbies and things she likes. Not necessarily related to the kids either.
You need to be doing 50% of the housework and parenting when you aren’t working, even if she earns less and is at home more.
You need to be doing more than 50% when she is unwell or not there.
Take the kids out of the house more often so she can have time alone in her own home.
Do not compete for her time over the kids (related to the dance class example of yours). You won’t win.
Accept that you will come second to the kids always.
Proactively parent. Who is the one organising birthday parties and gifts, extra curriculars, supervising homework, buying school shoes, sorting PE kits, applying for school places, making packed lunches, ordering school dinners, taking time off work when child is sick, reorganising life around child? From your post saying your wife does everything for all of you, I’m guessing she does the majority of this while you do very little and think your “gratitude” makes up for it. It doesn’t. Do 50% of these things from now on, and don’t ask for a list of what needs doing when. No one gave her a list.
When she finds she’s living with an equal partner and not another child, you may find your sex life improves. But the latter is probably a symptom of her being touched out, exhausted and resentful.