I think the issue may be one of the possibility of scandal (giving bad example) to those in your parish who know you are not validly married and who assume you are having marital relations. It might give the impression that your pastor approves of such arrangements.
I have heard that some pastors will allow persons in this situation, after a complete confession and currently living as “brother and sister,” to receive Communion at another parish where they are unknown and there is little risk of scandal. I am not sure what the official position of the Church is on this.
If there is not a compelling reason (for example, children) for you to remain together, it would probably be best to separate until you get the marriage issues resolved.
In the mean time, you can receive many graces by making frequent acts of spiritual communion. This is from an article by Archbishop Raymond Burke:
Our late Holy Father reminded us that the practice of making a “spiritual communion” comes from our deep desire to receive the Body of Christ. “Spiritual communion” is the expression of our profound and enduring desire to receive the Body of Christ. The act of spiritual communion prepares us fittingly for the time when we are able to receive Holy Communion.
Whenever we experience a period of time during which we may not receive Holy Communion because we are guilty of a mortal sin which we have not confessed in the Sacrament of Penance or because we are, in some other way, not properly disposed to receive, then we unite ourselves to Christ in the best possible way by expressing, in prayer, our desire to receive Him. God always responds to our act of spiritual communion with the help of His grace. Regarding spiritual communion, Pope John Paul II quotes St. Teresa of Avila, doctor of the Church:
“When you do not receive communion and you do not attend Mass, you can make a spiritual communion, which is a most beneficial practice; by it the love of God will be greatly impressed on you.”