Legal Question in Family Law in California

Wait until it is finalized. Ther are Automatic Restraining Orders which prevent you from doing it earlier.

Mr. Schneider is correct. By signing the petition for dissolution you, among other things, are saying you have read and will abide by all of the Automatic Restraining Orders set out on the Family Law Summons that will be served on your spouse. They become binding on you once you file the petition and binding on your spouse as soon as the summons is served. So you should read them asap.

There is no Summons in a Summary Dissolution, and likely no automatic restraining orders. In any case, prior to filing there is nothing requiring you to continue the health insurance, but it would be better to reach an agreement regarding payment for the health insurance until the dissolution is final.