If my branch manager has offered me to become a Drill Sergeant or decline orders and get out, what other options do I have?

SSG(P) (Join to see) DS, Recruiter and ROTC instructors commonly have the same mandatory fill requirements, you are not likely to get out of an assignment to one, but you might be able to horse trade and take a different one. It simply depends on the current business rules HRC is working under and the SMA's directive to branch managers.
I was serving as a Div G3 SGM when the SMA was having VTC's with MSC's to go over by name candidate lists...if you were on that list and not disqualified..Welcome to DS school.
But this may not be that, so ask branch.

That was the helpful part..
Here is the harsh reality
" SSG(P) (Join to see) If there are no other options then I would simply ETS at 6 years TIS"
With that and the limited info I know about your from a few lines of text.... Id say perhaps a better plan for the Army and you is to ETS.

Somewhere along the way you changed you mind, or otherwise no longer are interested in living the life you raised your hand for, which includes SELFLESS SERVICE: Put the welfare of the nation, the Army and your subordinates before your own. Selfless service is larger than just one person. In serving your country, you are doing your duty loyally without thought of recognition or gain. The basic building block of selfless service is the commitment of each team member to go a little further, endure a little longer, and look a little closer to see how he or she can add to the effort.

And its not a bad thing if you recognize that in your self and decide its time to go. You came, you served with honor, you earned the right to say your done. If you stay, please stay for the right reasons. If you go, do the same.
Give branch a call, worst that can happen is they say no deal, recruiter is not an option for you. If they do let you swap... thats not counter to selfless service which can include both getting what you want and what the Army needs.

There are no other choices. This is the way that every branch handles assignments. You're placed on assignment, you take the assignment and reenlist, or turn it down and ETS.
Also, there's no reason to believe that recruiting would put you closer at home or allow you to spend more time with you family.
This is actually a conversation you should have with your Career Counselor since you will be having it with them anyway.

I'd advise you go ahead and get the "punkin patch" and hat, then go on the trail. It's hard but very satisfying!!!