How will your income pan out over the next few years if all goes as expected?
Do you have security but not meteoric pay rise prospects (e.g teacher)
Do you both work now or is there capacity for you to go back to work and increase household income?
or what?
How old are your children?
What about schools?
Do your jobs come with pensions?
A house you can extend (e.g loft) may work out better value because you don't have to pay a new lot of stamp duty and moving costs - and your Council tax stays he same for a house you extend while you are still the owner.
Are prices rising fast in your area? Because where we are it has become harder to buy a bigger house, even with the increased equity, because the extra price bracket is so big in cash terms.
When you say 'not a lot' of disposable income, how tight would things be? To the wire and scrimping for every penny? Or comfortable - one not-extravagant holiday a year, the odd day out and eat out once every 6 weeks or so? Because spending 'a lot' of disposable income is money you will never see again and may be better invested in security, equity or savings for the future.
Running costs are higher on a bigger detached house: don't put yourselves in a potential debt situation.
If you can manage a life that is 'fine' but not extravagant and not put yourselves at financial risk, I would stretch to the detached house .