Yes, you can either cover the kids or the wife and the kids on your Family HDHP policy, and still qualify for the Family HSA annual contribution limit.
IRS Notice 2004-50 says,
"Family HDHP coverage is a health plan covering one eligible individual and at least one other individual (whether or not the other individual is an eligible individual)."
However, please note the following:
1. If your wife has a major medical policy, make very sure that you are NOT covered on it.
2. If your wife is going to be covered by a medical FSA, then you are NOT eligible to contribute to the HSA, because you cannot refuse to be covered by her medical FSA.
3. Once your wife is covered by the new insurance (whatever it is), she can no longer contribute to your HSA. Of course, joint funds are OK, but don't start writing checks from her account to your HSA unless you are a joint owner of the account.
4. If your wife will be covered by an HRA (Health Reimbursement Arrangement), make sure its rules state that you are not covered (I don't know if it's automatic like with FSAs.
Please see the section under "Other employee health plans" on page 5 of IRS Pub 969, for a discussion of what limited purpose FSAs and HRAs are permitted with HDHP coverage.
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