Do I have first rights to slaughter on the day I buy a child or parent animal?

Question

Rule:

וְשׁ֖וֹר אוֹ־שֶׂ֑ה אֹת֣וֹ וְאֶת־בְּנ֔וֹ לֹ֥א תִשְׁחֲט֖וּ בְּי֥וֹם אֶחָֽד׃

However, no animal from the herd or from the flock shall be slaughtered on the same day with its young.

If I purchase someone’s cow’s young [or vice versa] and we both want to slaughter today, who gets the right?

Answer 1

Shulchan Aruch Yoreh De’ah 16:6 writes that as soon as one sells an animal, he may not slaughter its offspring/parent that day, as the sale is done with the intent that the purchaser may slaughter the animal he has bought immediately.

שמיד כשמכר לראשון לא היה יכול לשחוט את שנשאר בידו שהלוקח לקח על מנת לשחוט מיד

Thus, the first right to slaughter resides with the buyer.

Answer 2

Tosefta, Chulin 5 (quoted by Rashi, Chulin 82a לענין; and quoted in Riff):

הלוקח מבעל הבית הוא קודם לבעל הבית שמתחלה לא לקחו אלא על מנת כן

One who purchases a cow from someone may be the first to slaughter, for that was his intention in buying it.