If one forgot Ya’aleh Veyavo in Shacharis on Rosh Chodesh, and then when it came time for Minchah he remembered that he must repeat Shacharis for a different reason, (e.g. mentioning or omitting rain in the wrong time) so he prayed a second time after Minchah in order to make up for that, but again forgot Ya’aleh Veyavo, would he need to repeat the Tefillah again, or not, being that it is a Tashlumin for Shacharis, for which one does not need to repeat once he prayed Musaf
First, Yaleh Veyavo requires repetition, if it was not fulfilled. Please see MB O"C 422:4 there where he states that one should repeat even after Mussaf with a conditional arrangement to satisfy the disagreement about Mussaf rectifying or not. But the Psak there appears to me to say that it should be repeated with that arrangement. I am not sure why the Tashlumin without Yaaleh Vayavo would change the matter?
I will say that Shulchan Aruch HaRav does not require one to repeat after Mussaf. Perhaps if you are Chassidic this would change the psak, this is why I think people do not offer Psak here.
I suppose you want to know whether the Mussaf mention of Rosh Chodesh can work if you said Mussaf before Shacharis (ie: the make up is said after Mussaf).
The best I could find is in O"C 126, B"Y
וכתב הרא״ש שאם לא הזכיר בתפלת המוספין חוזר ולא סמכינן על מה שהזכיר בשחרית דדוקא אתפלה שעדיין לפניו סמכינן ולא על התפלה שהזכיר בה כבר ולא סמכינן נמי על מה שיכול לומר במנחה כי דוקא בשחרית ומוסף שרגילים להתפלל כאחד
Here the B"Y mentions the Rosh that states that when one makes a mistake in Mussaf he needs to go back, he can only rely on a prayer that happens after, and not in mincha since that is not said together. That being said it would be worthwhile to check the Pri Magadim because I saw a quote that might imply he is more lenient.
Lamdus: So imo the repetition of the Amidah would depend on two things, is the first amidah for shachris batul then Mussaf can't help, for example it was wrong and NEEDS repeating or is it that something was missed and so to add that back in he repeats the whole Amidah, but the first Amidah was good and fixed by Mussaf. Yaaleh VeYavo might be like this (disagreement between Tosfot and Rif in Berachos - from memory).
TLDR: It should be repeated with a condition that it might be a nedava see MB mentioned above.