There are a few questions to deal with here, starting with the question of whether you were correct to wait until the morning to make Havdala. We will assume that your wife is fully capable of making her own Havdala.
It is true that it is preferable for a woman to hear Havdala from a man because of the opinions that she is not obligated in the performance of this mitzva.[1] However, if necessary, she may make her own Havdala. We will now investigate the issues that might make it preferable not to have waited for your wife.
All of the classical sources, from the gemara[2] to the Shulchan Aruch,[3] speak about making Havdala on Motzaei Shabbat. The idea that one may make Havdala until Tuesday evening appears to apply only b’di’eved (after the fact). However, one can claim that these sources just describe the normal situation where, of course, one should fulfill his mitzva within a reasonable amount of time and do not address a situation where there is reason to delay.
There is an interesting machloket between the Rosh[4] and Maharam[5] about one who was exempt from Havdala on Motzaei Shabbat because he was awaiting a close relative’s funeral. Is he obligated to make Havdala after the funeral on Sunday? The Taz[6] explains that the Rosh, who exempts such a mourner, understands that the basic obligation of Havdala is only on Motzaei Shabbat. Although one has until Tuesday to recite Havdala, that only functions as tashlumin (making up missed obligations) and is not part of the description of the basic obligation. In this case, as there was no obligation of Havdala on Motzaei Shabbat because of aninut,[7] he is exempt. The Maharam understands that the basic obligation extends beyond Motzaei Shabbat; for the mourner, it starts after the burial. According to the Rosh, it should be very problematic to delay Havdala until the morning, unless there is no choice in the matter (and, in this case, there is a choice). However, it appears that we accept the approach of the Maharam as halacha (based on Shulchan Aruch;[8] see Yabia Omer,[9] who discusses the various indications).
A further complication is that one may not eat or drink (except for water) before Havdala.[10] This is even the case upon awakening on Sunday morning, assuming one has the ability to make Havdala.[11] For Sephardim, there is yet another halachic concern. Three pillars of recent Sephardic p’sak (Ben Ish Chai, Kaf HaChayim,[12] Rav Ovadia Yosef[13]) rule that if one did eat before Havdala, he is able to make Havdala only if it is still Motzaei Shabbat.
Another thing to be considered by one who wants to delay Havdala is that only one who makes Havdala on Motzaei Shabbat can make the berachot on the ner and besamim.[14] Regarding ner, fire was created on Motzaei Shabbat. Regarding besamim, it is then that one needs to compensate for spiritual letdown after Shabbat is finished. At first glance, it appears that if one waits until the next day to make Havdala, he will lose these berachot. However, one may recite them independently of the rest of Havdala on Motzaei Shabbat.[15]
We conclude that it is halachically preferable for one not to wait until Sunday morning to make Havdala even if he refrains from eating and even if it means that his wife will have to make Havdala herself. Since both options are neither perfect nor halachically wrong, there may be circumstances where one will want to wait until the morning (except for the ner and besamim), while not eating.