Answer

Sometimes there are contradictions between the Guide and the Mishneh Torah, apparently because the works are aimed at different audiences and different purposes; this is an old observation. Perhaps attributing it to arousing jealousy would not have achieved the purpose for the perplexed readers for whom the Guide was intended, and so in the Guide he explained it according to the approach of mercy.
In general, his reasons for the commandments in the Guide are very questionable, and because of the force of the difficulty I have thought that all of them were said only in order to appease the perplexed.
I do not think it is worthwhile to build an elaborate harmonizing structure here if it is not even clear that these two sources need to be reconciled at all.
Still, a close look at the wording of the halakhah may perhaps yield a resolution:
 
Whoever says in supplication, “He who had mercy on a bird’s nest, commanding that the mother not be taken together with the young,” or, “that it and its offspring not be slaughtered on the same day, may He have mercy on us,” and anything similar in this matter, is silenced, because these commandments are scriptural decrees and not mercy. For if they were because of mercy, He would not have permitted slaughter to us at all. Likewise, one should not multiply divine epithets and say, “the great, mighty, awesome, strong, valiant, and powerful God,” for human beings do not have the capacity to reach the end of His praises; one says only what Moses our teacher, peace be upon him, said.
 
Maimonides connects here the law against multiplying praises with the reasoning that we cannot reach the end of the Holy One’s praises.
At first glance, that reasoning does not negate that those praises are correct, only that they are not fully precise, or that if one multiplies them one may compare Him to human beings.
Accordingly, perhaps with the bird’s nest too, the reason of mercy is indeed correct, but not precise. There is also a decretal dimension to it, something not fully human—and the proof is that slaughter was permitted. After all, slaughter too is carried out with concern for animal suffering, so clearly the proof is only that describing Him as merciful is not a complete description, not that it is false. Especially since it involves anthropomorphism.
Therefore, one who says this in prayer is silenced, because he is saying something imprecise. But attributing it to mercy in itself is indeed correct, at least by way of the negative attributes described in the Guide, and therefore in the Guide he does explain it that way.
And it still requires further examination why in the Guide he wrote that this was said according to the view that there are no reasons for the commandments, and did not explain it as I have suggested here.
Therefore, it seems more likely as in my earlier answer.