Simple answer is that the taxpayer (who funds the RAF) won't pay for you to visit your children.
If you have custody of your children (centre and prime mover of them) then you would qaulify for an FQ, and relevent allowances including Boarding School Education Allowance.
As for your situation, apart from good management by local commanders some units fund the provision of placement accommodation out of Service Funds (ie not taxpayers' money, but our own - for any journos peeking) which can normally be used for a very nominal fee. That way you can have you children visit you and not try and cram them in your room in the block/mess or use an expensive local hotel/B&B.