Aiden,
Sorry my late reply.

Financially, the UKBA are interested in your non-disrectionary expenditure. Means Mortgage/Rent/Property Secured Loans/Council Tax
They are not interested in any discretionary expenditure. EG you make by choice ( ie food clothes phone gas water leccy internet etc)

£250 per month rental for 3-bed house is going to be a big ask to fulfil, certainly in our area. If you can do it great. But please reconsider this.

If you have some family able to help with accommodation or even financial that will be a big help for you.

UKBA say:-
Maintenance may be provided by either:-

The applicant with their own funds or with funds available to them; Or
The sponsor; or
A combination of applicant and sponsor funds; or
Third party support (from family members). The ECO may request evidence (for example, original bank statements over at least three months) of the third party's assets. Third party support is not precluded from consideration under the maintenance requirements relating to Spouses.

Solely from the basic information you have projected, the financial side is marginal.

The ECO will need to feel comfortable with the 'complete application' and not just one or two elements.

Aiden, you may find significant benefit in seeking specialist immigration advise to help with your overall strategy, presentation and/or application.

There's a number of reasons why I suggest this:-
Your particular case is multi-faceted, and not the usual very straightfroward case.
You may be entitled (in your name) to claim some benefits such as child benefit, Child tax credits etc.
Your wife will be allowed to work as soon as she enters UK (may help financially)
If you and your wife have completed 4 years living together outside of UK then she may well be granted Indefinitie Leave to Enter. This means that she will not need to complete the two years probationary leave in this category before applying for indefinite leave. Rather she can apply for ILR immediately following her Life in UK Test. This in itself can ease the financial requirements as your wife would then be entitled to claim benefits as well.
Two of your children are British passport holders and as such do not need to apply for entry visa. It's quite possible that they could enter the UK with you.
Depending on your arrangements when you and the two children arrive to UK, there could be some ways to ease the 'financial test' when your wife makes visa application.
There are a number of recently reported judicial decisions (case law) that may be helpful for you.
The immigration specialist may have some ideas for you about this.

I hope I'm not making it sound overly complicated. It's certainly not my intention.
For all these reasons (and possibly a few other special personal circumstances) I'm confident that with good specialist advice and a number of potential caselaw examples you maymay be able to put it all together.

Finally, I have no ideas how immigration rules may change in the future, but I suspect that your case would not be any easier.

Hope this gives you more food for thought.