Thank you for the new question.
Yes, you are going to be asking them to extend the regular coverage as part of your severance instead of COBRA.
In regard to how long COBRA coverage will extend, the general rule is 18 months. If within that 18 months, your child becomes entitled to Medicare, then COBRA coverage can be extended up to 36 months for your child.
Additionally, if your child's condition qualifies as a disability, which it probably does, then the COBRA coverage will be extended to 29 months from the date of your termination
. To obtain this extension you must obtain a disability determination from the Social Security Administration. You would contact the nearest SSA office and ask them for the procedures and forms you need to request the determination.
The Affordable Care Act (aka Obamacare)'s regulation which provides coverage for pre-existing conditions comes into effect in 2014, so even a simple 18 month term in COBRA will provide you with enough time until the law comes into effect. At that point, you will be able to locate an affordable policy which covers your daughter.