Today, I found out my girlfriend, a project manager, will be in charge of another project, for which 2 - 3 members of my team will be needed. All in all, I will have now lost close to half my team during the life of the 2 projects. Ad nauseam, the same HR solution I wrote of before of having team members on projects led by my girlfriend be removed from my vertical reporting stack will be used to mitigate the conflict of interest between my team members' horizontal manager (my GF) and their vertical functional manager (me).
Two new developments occurred this week:
Team members complained to me the removal of colleagues is affecting their day to day work and want a replacement resource. Privately, a team member said instability would be a factor in deciding whether he would want to look for another job.
My manager in my 1:1 said he wants me to take on more responsibility.
Due to budgetary constraints, backfill for team members reporting vertically to my GF is highly unlikely to infeasible. I realize this unpleasantness is my own making and the result of our romantic relationship. It's painful to think that this messiness may lead to relationship breakup.
How can I push back against management request to take on additional tasks, at least until I get new resources?
Should I admit that my team's output may suffer or would this be an admission of incapacity, weakness, and bad judgement (i.e. Dating coworker in the first place)?
How should I respond to team member who hinted he may be looking for a new job due to team structural instability? Do I need to be completely honest as I feel my dating life is of no concern to him?
Edit: Some answers are saying that the relationship is not relevant. To clarify, when team members on project are removed from my vertical reporting chain, I lose my entire ability to direct what they do, at least during life of the project. If I am not dating the PM, I retain vertical supervision , and hence can at least have a degree of supervision over team members reporting horizontally to my GF. It's the prohibition by HR of me having any supervisory influence that's the root of the problem. Traditional two manager reporting style in matrix management organization is not feasible here due to HR imposed constraint.
Also, both of us want the relationship to work, and only want to consider breaking up if push comes to shove.