No doubt, Hajj is a golden opportunity to have one’s sins forgiven, one’s soul refined, and one’s heart filled with iman and tranquility. The one who performs Hajj is supposed to be a model for others after returning. He or she is to recall throughout the year the matchless experiences gained in Hajj.
Dr. Sabri `Abdur-Ra’ouf, professor of Islamic Comparative Jurisprudence, at Al-Azhar Univ., states:

“We should stress the fact that those whom Allah favored to perform Hajj and `Umrah, should be thankful to Allah (Glorified and Exalted be He) Who has chosen them from among His servants to perform these acts of worship, and they should implore Almighty Allah to accept their good deeds. That is very important, for it reflects their belief that being so favored by Allah to accomplish the task of traveling to the Sacred Land to perform Hajj and `Umrah is a favor that deserves gratitude to Allah.”
In his answer to your question, sheikh `Abdel Khaliq Hasan Ash-Shareef, a prominent Azharite scholar, says,

“There is nothing wrong with that. Taking into consideration that you are performing Hajj tamattu`, there is no harm on you going and performing `Umrah and returning home, and after that you go to Makkah again and start Ihram anew on the day of Tarwiyah.

Moreover, during the interval period between your Hajj and `Umrah, you are not regarded as muhrim (in the state of Ihram). That is to say, it is permissible to you during this period to wear sewn clothes, have intimate relations with a spouse, etc. Only, when you start Ihram for Hajj, such things becomes unallowable to you.