Hi newenglander from a fellow New Englander!
Welcome to UKY. There's definitely some great information here and some truly wonderful people.
I'm in a similar situation (no kids, though, so I can't speak to that point). My husband and I have been married for nearly 7 years in the US.
You are eligible for ILR (or ILE, which is the same...just depends on if you receive it outside the UK or within). If you are heading to the UK for a holiday before you apply, you can take the Knowledge of Life in the UK test and when you pass, you can submit that with your application for a spousal visa and be granted ILE right away. This is what I'm doing when we go for a holiday over Christmas. We're going anyway, so why not take advantage.
Another option is to apply for a spousal visa and I think you request that you have KOL required added. That way, when you enter the UK on the visa, you can take the KOL test and when you pass, apply for ILR from within the UK.
The difference is a matter of paying for the spousal visa AND the ILR
OR paying for the price of a plane ticket to the UK and the spousal visa that has ILE. Which is why if you are heading over before you apply anyway (not sure if you are or not), it's better to take advantage of the situation in that respects.