If the sauce is used to cook the chicken in, then I would have no concerns about freezing the leftovers. I make various recipes that include a dairy based sauce of some variety - yogurt, sour cream, even heavy cream - and after cooking, the leftovers freeze perfectly well. Uncooked dairy may not freeze well (although I have no issues with cheeses or butter) but dairy used as a component of a cooked sauce freezes just fine. I find no deterioration of texture, splitting or separating or loss of flavor.

Yes, raw but out of the shell will be OK frozen. You just don't want to freeze in the shells and your pups have taken care of that already. "Once you’ve cracked open the eggs, pierce the yolks, mix them to blend with the whites, and then add in either of the following: (1) one-half teaspoon of salt for every cup of raw eggs, if you’re planning to use the eggs for savory or main dishes; or (2) one tablespoon of sugar for each cup of eggs, if you’ll be using them for baking or desserts. The salt and sugar both work to prevent the eggs’ yolks from becoming too gelatinous once frozen."

There are rules for safe pressure canning. Many cooks add a lot of low acid ingredients to their spaghetti sauce (peppers, onions, mushrooms, meat, etc.) so there could be a world of trouble in improperly canned spaghetti sauce. I boiling water bath a basic seasoned tomato sauce and add the low acid ingredients later, before serving. Or, if I want to make a big batch of spaghetti sauce with low acid ingredients ahead of time, I freeze it. Considering how easy it is to make spaghetti sauce from scratch with seasoned tomato sauce, I can't imagine why I would make a big batch ahead of time and use up freezer space for it. YMMV. I have a relatively small freezer . . . I use it mainly to store meat I get on sale and excess baked goods, plus beans and some other vegetables I don't pressure can. Tomato products I boiling water bath using approved recipes. It's not that easy for me to pressure can at my house with a carpy electric stove . . .

I do it all the time for use with poultry year round. In October when the cranberries first hit the stores, I reasoned they were at their freshest from harvest and bought over ten pounds to freeze. I freeze the whole bag, i bought two pound bags. Then I make the same recipe as you do, stir everything together and let it mascerate for about a half hour. I freeze it in 8 ounce freezer containers. When I am ready to use it, I take it out a few hours ahead to defrost or even defrost it in the refrigerator a day ahead. I would be surprised if you could find fresh cranberries in the stores now. They are out of season here in California till next October. I love to stir a spoonful of the cranberry relish into plain or vanilla yogurt too.