I am thinking of opening a solo 401k and contributing to the Roth 401k portion of the account. I am also trying to find out if I can then "hire" my children during the summer (they are 2 and 4 years old), but most of their "earned income" from myself employed business into their roth 401k and then have them use it for college tax free. Can I do this?

Just so I'm clear on this - you would "hire" your kids, pay them an hourly wage, issue W2's to document their "wages," withhold income tax, social security, medicaire, and state/local income tax (if applicable) from their paychecks, right? And you're going to deduct as business expenses the wages you pay them when you file your taxes? I suspect that when the IRS audits you they'll have a few questions as to the specific work that your 2-year old and 4-year old did. Having phatom workers on the payroll is a time-honored tradition in some places (I live in Chicago where our elected officials seem to do this all the time) but I would not recommend it - it can lead to an extended time as a guest of the government, with room and board at tax payer expense (as so many of our former officials have discovered).

In my opinion, apparently your personal tax related goal is to get so called positive sum game like results; good for both yourself and your children. What I mean is that you want to avoid "Kiddie Tax rule" by shifting earned income in lieu of shifting unearned income to your children( by hiring them as your employees to pay them wages or salaries, earned incomes for the children, and putin' it in their R401K accounts) ,and this, when shifted to your children by satisfying related tax rules, will also decrease your tax liability and AGI.( as you can see, numerous income tax provisions, especially the new ones enacted through the Taxpayer Relief Act of 1997, are phased out as your AGI increases.So lowering your AGI relatuvely increases your eligibility for a number of these tax breaks. You see that, don't you?)
Butin general, hiring 2 Y.O. and 4 Y.O. little children, paying wages, issuing W-2s for payin' FICA Taxes doesn't seem to be somewhat rational . Of course there are little children earning earned income and maybe paying either FICA or SECA taxes; little 1 Y.O. or 2 Y.O. children models hired for Huggies or for children's foods ads. Or etc.
Except this sort of extraordinary case, in general, hiring and paying wages to little children can invite attention from the IRS... then you need to explain as to the specific/characteristic work done by your children.

Both ebaines and wnhough bring up very valid points.

You CAN hire your children and pay them wages for work done for your business! It just has to be VALID jobs where they actually work, not "phantom jobs".

Wait a few years where they CAN do things like clean up your work space and do simple filing, then re-visit this approach.