a family visit/tourist visa is no problem....
in addition, if your named on the kids birth certificate, the UK technically has to uphold your human right to a 'family life', so in effect, MUST allow entry and stay.
That's the route I'm going to take in case all else fails in the future.....
once you have the first '2 year limited leave to remain' and id card, the renewals should be a simple formality as your on the system as legal. The first is the hardest, tho this is only my thoughts, im no authority! we have had two now, but were married in uk and have securities there.