I had heard that non-Jews are not allowed to join the Seder. If someone has a non-Jewish worker who would be offended by being excluded from the Seder, can she be invited out of "darchei Shalom"? Does it matter if the worker is an evening hirer (hired for only the Seder meal) or a live-in worker?
The main point is that one is not allowed to cook for a gentile on Yom Tov. As a result, one should not invite a guest. A maid or waiter can be served because they will not expect extra food to be cooked for them.
May one invite a gentile on Yom Tov to eat at the Yom Tov table?
There definitely is a serious problem in inviting a gentile, on Yom Tov, to partake of your Yom Tov meal, for the following reasons:
The possuk in (Sh’mos 12:17) states 'ach asher yochal l'chol nefesh hu levado ya'aseh lachem', which teaches us that one may cook on Yom Tov for the sake of Yom Tov. However, at the end of the possuk the word לכם – for you, the gemora explains, means that one may not cook or do any melacha for a gentile. This means that one may cook and roast chicken for a Jew on Yom Tov, but not for a gentile.
What could be wrong, if for example the food is prepared in a single pot?
Chazal prohibited preparing food for a gentile on Yom Tov even though one is cooking it in the same pot without any extra effort. The question becomes more difficult when the Shulchan Aruch HaRav  points out that the halacha states that one may fill a pot of water and boil it even though one only needs the amount of one cup and the remainder will be used after Yom Tov.  (One may not say that the excess is for after Yom Tov and it may only be filled in one occurrence). If so, why is it ossur to cook extra for a gentile even though there is no extra effort invested?
The answer is that when one invites a guest over to eat, one makes sure that there is ample food for one’s household and for the newly arrived guest. Chazal were afraid that one would cook extra food for the guest in a separate cooking pot and thus violate the issur of cooking for a gentile. Therefore, even though one does not intend to cook in a separate pot for the gentile, there is reason for concern that it might lead thereto. 
Does that mean that I may not give my Yom Tov food to my gentile maid?
No, it is not the same. The reason for the distinction is because one’s maid is not a “guest” and is not treated with the same honor. One would not cook extra food in a separate pot for the maid and therefore there is no room for concern. However, one may only add extra to the pot in the first place before the initial cooking but not add to the pot after it is already on the stove even for one’s maid.
There are exceptions to the rule, for example, certain dishes have a better taste when there is more food in the pot, which would permit adding food to the pot even after it is on the stove, but a rav would need to be consulted because this does not always apply. As mentioned, the optimal is to add as much as necessary to the pot before cooking.
May I invite the guest on Yom Tov after the food is prepared? It seems that then there is no room to be concerned that I will cook more food.
Even in this case it is forbidden to invite a gentile. 
What if the gentile arrives uninvited?
If the guest arrives after your meal is already prepared the person may partake of the meal. If however the person is a VIP, there are those who prohibit this unless you explicitly say to the guest that he may share whatever you have prepared. Even if the person arrives of his own accord, you may not coax and invite the guest, because that is similar to an invitation. 
 Simon 512:3.
 Shulchan Aruch HaRav simon 503:4, Mechaber 503:2 and M”B 14-15.
 Shulchan Aruch HaRav simon 512:3.
 M”B simon 512:3. See the Sha’ar Hatsiun 3 who argues with the M”A who permits this, because from the Rambam one sees that even this is ossur.
 M”B simon 512:10.