In short: if you can you should apply for a PR soon, and convert it to a settled status once it's available. However it's possible that you'll need the support of your partner both times.
Based on the current details on how the settled status will work, it will be easier to obtain that than the Permanent Residence document, and will also be valid after 31 December 2020, which is the current validity of the Permanent Residence documents. However things might still change - although politicians did promise the scheme will go ahead, it's not yet fully a law, and a no-deal Brexit could (although unlikely) still change the scheme. A no-deal Brexit might also mean that the validity of the PR documents will also be reduced to 31 March 2019.
However to be safe, and if you're already eligible for obtaining a PR document, you should apply for one as soon as possible. Converting it to a Settled status will be free, and it will likely be easier as well, although based on the government's website you still need to prove your relationship to your EEA partner when doing that.
If your partner is not eligible for the PR status - likely because they can't prove that they have worked for the past 5 years (or have Comprehensive Sickness Insurance for the period where they haven't been working), then you'll need to wait until the Settled status scheme opens after March 2019, as it will drop this particular requirement.
In both cases it's likely that you'll need the support of your EEA partner, so if they are reluctant to help you now it's likely you won't be able to obtain either of the documents. If they are helpful now but are worried this won't last until the Settled status scheme opens, it's still better to obtain the PR document soon. Although currently the government's site says you'll still need to prove your relationship when you convert the PR to a Settled status this requirement might go away. Even if it's not you'll have a document that allows you to stay in the country until December 2020, until which time you might be able to get a different visa, or an ILR.
Also note that once either you or your partner obtains either the PR or the Settled status, your existing UK born children will be immediately eligible for registration as a British citizen. However it's not automatic, is fairly costly (£1012 per child as of November 2018), and it's only available if your children's other nationality permits dual citizenships, but it would make your children safe from the immigration aspects of Brexit. Also note that any new UK-born children after you obtain PR/Settled status will become British citizens immediately - no registration is needed - you can use your PR/Settled documents to prove their eligibility for citizenship.
