Ok wow there's a lot there and you are kind of entangling 'fairness' with being 'sensible' but also protecting yourself in the event of divorce/death - none of these are mutually exclusive but they are all subjective concepts, won't mean the same thing to everyone and may lead to slightly different priorities and decisions. So for me regardless of if you are taking the lead on this in your relationship and/or your DH isn't really bothered you are going to have to ensure you communicate well and make decisions jointly...
I think I'd start with three things, one is a proper and full financial audit of your circumstances, taking into account incomings (not just your DH's salary but any benefits, income from assets etc), existing assets and an agreed budget for outgoings (this is where communication and agreement with your DH comes in as if he's a high earner and used to not thinking about money the concept of limiting his spending may be alien to him). I'd include absolutely everything in the budget, mortgage, bills, cars, holidays, entertainment, clothes, hobbies (Money saving expert have a great tool for free) and agree how much you each have as 'spending money' - as a SAHM you may find yourself tempted by a huge amount of baby classes, outings, lunches/coffees etc. at the very time your income is actually decreasing and this can be a major source of relationship tension so you def need to both be on the same page on this as well as other things to do with the children's budget.
Second I'd look at your various long term financial goals and how much you need to save to achieve these, having an emergency fund in case of disaster, job loss etc seems very sensible before you look at anything else, 6 months income is the standard, I'd add getting life insurance and potentially critical illness and income protection cover to that as well. Then you mention other goals, pension/retirement planning, paying for school fees etc (school fees are extremely expensive these days so you may perhaps need to cut your cloth with other spending accordingly) - you may want to take some financial advice esp on the pensions as you want to minimise the tax you pay there so a SIPP or similar for you might make a lot of sense.
The third thing is to see a solicitor re wills and how to set up ownership of your assets - it's pretty standard for one spouse to want to leave assets owned before marriage or acquired through inheritance in trust for their DC or whatever rather than absolutely to the surviving spouse esp in case of remarriage but there's no 'automatic' about it, it depends on how the ownership is set up currently and your will, you need legal advice really. Equally, in case of divorce you are fairly well protected as standard as the norm is for all assets to be divided regardless of whose name is on them (e.g. his pension could end up having to be shared) but again it can get complicated with some things being pre-marital and a potential big windfall coming through his business so again some legal advice would be sensible...