There is another phasing tool you can use if you have other known relatives of your father you can bring into play; your own children and half-siblings won't really help here. It's a GEDmatch Tier 1 tool, meaning you'll need to pay for at least month month of service in order to use it, but it's cheap.
Once you're logged into GEDmatch, you can use this link to read about the Lazarus utility: https://www.gedmatch.com/gedwiki/index.php?title=Lazarus. It's a bit more complex than the simple parent phasing tool, but offers more flexibility--and potentially greater accuracy--because of it. With the right combination of relatives' test kits, it can even be used to synthesize "pseudo-genomes" for long-passed grandparents. But it requires advance planning in the form of preparing a list of the kits on GEDmatch you want to use.
There are three places kit numbers will be entered. The first is optional but, similar to the regular phasing tool, brings your mother into the evaluation, which helps. The spouse's kit entered here must be the parent or grandparent of all the direct descendants in Group 1. And that's exactly what Group 1 is: direct descendants of both your father and mother (if you enter your mother's kit). You can enter up to 10 kit numbers here; this is where you'll put your own kit number. Your three children could go here, but there's no advantage to it, and GEDmatch recommends using only the closest direct descendants (if you had a full sibling, you'd use him or her, as well).
Group 2 is the trickier one. You can enter up to an overwhelming 100 kit numbers here. It looks like overkill, but the more the merrier if you have no close relations to your father to use. Group 2 is for relatives--but not descendants--of your father, the target of the pseudo-kit. Generally in order of best-to-use: parents (which I've never yet seen available for a Lazarus run, but there it is); full siblings (your aunts or uncles); aunts/uncles or nieces/nephews of your father; and then cousins in descending order of closeness. The key here is that the people entered in Group 2 should have no biological relationship to you mother. If you aren't solidly convinced that a cousin of yours is not strictly from your father's side, don't use him. Mixing in maternal cousins will foul-up the resulting pseudo-kit.
In the segment threshold settings, if you've been able to use one of your father's siblings, aunts/uncles, or a couple of 1st cousins, I'd choose "7.5 cM 50% Real Matches." If you're only able to add cousins, I'd stick with the default "6.5 cM 25% Real Matches." If you start at 7.5 and the trial run doesn't provide at least 1,500 cM in the resulting kit, you can drop it to 6.5.
The processing options offer a trial run, no batch processing, and full processing. Do a trial run first. You're shooting for a kit that contains at least 1,500 cM in shared segments; that enables the kit to go through full batch processing so that it's available to use for one-to-many and other multi-kit comparisons. Less, you can still generate a kit but you can use it only in one-to-one comparisons.
The final caveat from GEDmatch my cause your head to tilt: "the resulting surrogate kit does not contain any SNPs for segments where there was no reference data." Hmm...
Since GEDmatch uses raw data from different test providers, they're actually comparing oranges and tangerines: the various test providers don't all record the same SNPs. For example, 23andMe tests using the new v5 GSA chip can't be used in the regular GEDmatch at all because the SNPs tested don't align with the older Omni chip and the results from the other testing companies (yet; they're all going to have to go the GSA chip). Ancestry v2 results provided about 650,000 SNPs when uploaded to GEDmatch; 23andMe v3 tests had about 640,000 SNPs that could be compared to Ancestry's; and 23andMe v4 tests about 300,000 SNPs. So it's only a true oranges-to-oranges if you're looking at two kits tested at the same company under the same chip version. That's what GEDmatch means with that cryptic sentence. If, for example, you're working with one kit from AncestryDNA v2 and one from 23andMe v4, there are only about 300,000 in play because the others tested aren't in the same locations. Lowest common denominator. For phasing, including Lazarus, the new pseudo-kit can contain only information about the SNPs that could serve as reference data. But don't let the mumbo jumbo scare you off trying Lazarus. It's just something to keep in mind if you can't hit that 1,500 cM threshold.
