A lot of people including op seem not to have heard of the 7 year itch!
Why 7 years? Because its at that point most couples are dealing with the multiple demands of a young family, ageing parents, demanding jobs and money worries.
Divorce rates peak around this point.
But it's generally considered to be a rut and can be recoverable WITH effort.
"Sex life is poor perhaps every 4/5 weeks but it has been since we first got together. That's me; always had very little interest. He knows no difference from me" there's a lot of support (and rightly so) on mn for women not to have sex if they don't fancy it BUT the fact is the difference between a friendship and a relationship is sex! It helps couples to bond and connect and is imo very important. Not necessarily every week but I'd say most weeks at least once at your and your h age certainly is closer to normal imo.
"My father is terribly ill and he's therefore my priority and the children obviously." I would say you were a little quick to dismiss suggestions of depression, particularly considering the stress you're currently under. Ignoring your MH And not prioritising your marriage are not good ideas long term. Investing in your marriage is also part of prioritising your children, fact is (and I speak as a single parent of 16 years) that children generally, where there's no abuse, do better in 2 parent families, lots of reasons for this.
"I do probably 70% of house stuff but it's my house (bought before we got together) so I feel that's only fair." But it's the FAMILY home and he lives there and makes the mess and your (joint) children make the mess. He needs to step up and make a fair contribution to your HOME and family.
Being responsible with money is one thing. Avoiding spending to the detriment of a healthy fulfilled life is not actually being responsible. And you don't need to spend a lot of money to enjoy yourself. There's a phrase I think you need to understand and accept
There's no pockets in a shroud!
Life is short too short so if you possibly can you should make it as rich as possible.
Babysitters - kids must be under 8 possibly younger. Could you look unto nursery workers or TA's they and you are familiar/comfortable with to hire as sitters? Or any friends with teens or friends who could sit and you return the favour? (This imo is what sleepovers are REALLY for) just read you're a teacher, you MUST know via that a TA or someone who could sit?
Re dh birthday, why not post on here for ideas? Say his age, interests, job and hopefully some mners will come up with ideas. I certainly do that for my difficult to gift people.
What help are you providing your brother and patents? Could someone else provide that help either via govt/charities or paid for? How are your parents finances? My parents are in their 70's and in poor health but are comfortably off and happy to "throw money" at certain issues to make them easier. You wouldn't necessarily need to spend less time with them, but could then spend that time relaxing with them rather than doing jobs.
And yes get in help at home too! There are no awards for being a martyr, you're obviously intelligent, caring and thoughtful but you been to be more mindful of your MH (and physical to be honest) and of nurturing your relationship.
Sex has other benefits too, boosts mood, helps sleep quality and is good exercise.
I hope what I've said is taken in the manner intended which is genuinely wanting you to be happier with your life and relationship.