All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If the questioner means by the "intention to gain the blessing" the blessing resulting from making up for the missed days on a blessed day or the blessing of observing fasting itself, but she does not mean thereby the intention to observe the voluntary fasting on the 9th and 10th of Muharram, which is an act of the Sunnah, there will be no harm in combining the intention of making up and the intention of getting the blessing. However, if she means by the "intention to gain the blessing" the intention to observe the voluntary fasting on the 9th and 10th of Muharram, this will be considered combining the intention to observe two independent acts of worship each of which is required to be done individually. In this case, combining is not valid.
Allaah Knows best.