Yes, given the facts you've provided, you will be eligible to contribute to an HSA. Eligibility is determined by the insurance coverage that the individual making the contribution has, not by coverage that other family members have. Since you would be covered by an HDHP plan and you would not also be covered by some disqualifying coverage, you are eligible to contribute to an HSA. Some of your children being covered by other insurance that is not an HDHP has no bearing on your own eligibility to contribute to an HSA.
If the HDHP plan covers both you and some other family member, your contribution limit will be based on having family HDHP coverage.