Why that specific group? Why not the wealthy? Or the poor? Or women? Or landowners? This sounds like a terrible idea, along the lines of the government subsidizing home ownership the way it does in the US. The only version of this that I've seen that I actually liked was the idea that to declare war a referendum was necessary (can easily and quickly be orchestrated nowadays) and that the people that vote Yes are the first to be drafted. Naturally, only the people eligible to vote are the ones eligible to serve. I think almost everyone can agree that war is bad, while I doubt that we can all agree that choosing to be between 35 and 60 and have kids is the most ideal state of being for the country/economy/the world.
The reason why that specific group was chosen is that they represent non-voting citizens. There are 73 million Americans too young to vote. They are subject to laws and pay sales taxes, but have no representation in the government. The proposal isn't a "reward" for being a good breeder, but an attempt at rectifying that almost a quarter of the population has no electoral power. I believe that the age range was mostly chosen to ensure that these are parents of children who are not of voting age, but I think it would be easier to allocate one vote to each social security number and let parents proxy vote for their children. Honestly, I'm not sure that this is a good idea, I'm not sure that it's any worse than just denying representation to a segment of the population.
My other concern is your policy on referendum for war. I'm opposed to war and would vote no on pretty much any referendum. However, I also have cerebral palsy and am completely ineligible to serve. Do I not deserve a say in our foreign policy? Also, the US has gone through its past few wars without instituting a draft. My more bellicose relations would be able to vote for this war without any serious fear of being drafted.
I think the much bigger problem than the minors not being able to vote would be the problem of apathy. 3/4 of American voters don't vote for whatever reason. Of the 1/4 that do, most don't know foreign policy from a strongly worded statement about Christian values. The reality is that voters are much easier to influence than they imagine and elections are not won on the fundamentals of the party but on the way that the team spins the personality of the candidate.
Now, as for the referendum thing... It's not my idea, I'm paraphrasing an idea that is twice as old as I am. I think it can be tuned and refined. The idea behind it is that war should be declared only when a majority of the country's draft-age people are willing to lay down their lives for the cause. What we have now is that a few hundred people get to decide to send a small minority that is the military into harm's way based on any reason they want. Making people more directly responsible for declaring war is a good idea.
You are right in that we have not had draft for the past few conflicts. Also remember that the United States has not declared war since WWII [1]. The rest of these conflicts were not wars but "military engagements". And the military probably does not want to get an influx of draftees who have no idea what they are doing either. They are going to be much more likely to die in the conflict due to lack of training, etc.
All that aside, I think the idea here is more valuable than implementation. The idea that if you decide to do something so major as to declare war on a foreign country, you should feel the consequences more immediately. Perhaps if you vote yes, and the majority wins, then your taxes are raised to pay for this war. Or maybe if you vote to raise taxes, then your are raised by double of what you voted for one year (not for/against raising taxes, just using it as an example of a major change).
"subject to laws and pay sales tax" is a broad argument. Tourists and legal residents do the same, but have no representation.
Granted, that's a nit pick. What's much more serious is widespread (and horrible) practice of disenfranchising adults who have been convicted of a felony. There are some 6 million adult Americans citizens who have no representation in Congress.
And it disproportionally affects blacks. From a couple of years back: "In Virginia, 20 percent of blacks can't vote. In Florida, that number is 23 percent. ... (Kentucky, which is safely in Republican hands, is the only other state where 1 in 5 African Americans can't vote.)"
I see a bunch of difficulties with the proposal (if the parents are felons but the child is not, can the parents vote? if the parents are divorced, who gets to control the voting right? what of children in foster care? if the child is mentally disabled, with the cognitive state of a 1 year old, then can the parents still vote? Why is the scaling factor 1 instead of, say, 0.5?)
These can be worked out, and civil rights shouldn't be ignored just because "it's complicated." But the proposal's doesn't feel right. If a felon can be disenfranchised, then that felon no longer has representation. If representation is that important for a non-voting child, then surely it's that important for a non-voting adult. So shouldn't some other adult be able to vote on behalf of the felon?
BTW, you might be interested in Mark Twain's short story 'The Curious Republic of Gondour."
(Also, your 73 million number is a bit too high. I came up with 70 million, based on the census numbers minus the number of non-citizens living in the country, and adding the number of citizens living outside of the country, then scaling the sum by the percentage of people in the US who are under 18.)
The problem with the concept is not that it's inherently a bad idea to temper democracy, it's that it will become just another way of gerrymandering: Make it easier/harder to people you agree/disagree with to vote their mind to stack to deck in favour of a given outcome.
The two are one and the same. Every time you introduce a crude new exception to the rule, you create an imbalance and complexity. Simple is better than complex. Organic is better than artificial. Otherwise emergent behavior is always a way to hack the system (e.g.: gerrymander). The beauty of one vote per person is that it's simple. Now, in the US, things get complex when we start talking about swing states, the fact that 3/4 of voters don't give a crap, etc. You can easily have a system where a few thousand Ohio residents decide who becomes president. However, the more complexity you introduce the more loopholes you will create.