I believe companies are required by state law to offer COBRA insurance.  Instead of the company paying most of the premium, you can keep the same plan but pay the company portion (quite high).  Or you could get other insurance.  Or, of course, you could live on the edge and go with no insurance for 90 days.  The biggest problem you'll run into is that your court order probably says that you are obligated to provide the insurance.  It doesn't say what kind of insurance, just insurance.  Maybe a very cheap major medical plan for the kids for 90 days would suffice.  It's not my place to advise you on what kind of insurance you should/shouldn't buy, but I think the courts "could" hold you accountable if you're supposed to provide the insurance.

Yes, I would believe so.  In fact, I think you have a strong argument that would be the most cost-effective option as well.  Of course you want to communicate this to mom so she knows she must maintain insurance until yours kicks in.  Written communication which is sent certified mail return receipt is usually best for things like this.