Does SQL Server have any solutions that will help me with this?
It's not easy to say. These things need in-depth study and no one on the internet can properly tell you something that really helps.
As far as I know there is nothing ready in SQL Server. It has a number of features that used together can make it a little easier, but you will have to create your solution, it will be laborious.
I reinforce that the first step is to have the problem very well defined, to analyze everything that is going wrong.
Even with the correct diagnosis and prognosis, when you are deploying, you may find that it does not work as expected. So it's tricky to point out that you should use something.
Is working offline in my situation ideal?
Only you know it. Is everything working well? So it seems to be enough. You do not have to look for the ideal if you are attending to everything.
Are you having problems? So you need to diagnose in detail what is happening and then look for prognostics.
Which way to go?
Again only you can answer this, any answer that tells you the way to follow will be only an opinion, it will have no relevance whatsoever.
Roughly you have to build your application so you do not depend on the central database to be working. Whether this is feasible or ideal I do not know. But this is certainly necessary.
If you can not solve the infrastructure problem you will have to give up something. It may be that synchronization, if well done, does not cause any major problems, but it may be that it will not make some things you want.
There is no miracle. Just as you can not run the latest World of Warcraft on a 386, you can not maintain real high availability with poor infrastructure.
I doubt you can solve the synchronization problem with SQL Server features only.
Of course if in the background the databases are decentralized in the units and only concentrates the data centrally (does not seem to be the case by the report) there it is easier. But I think you're already doing this. Maybe you do not accept the drawbacks of this but I do not think there is anything that can be done other than ensuring good timing.
I assume you have already read documentation . I have doubts if any of them solve your problem. I think you've noticed that.
I'm sorry if this does not exactly answer what you want but it's not easy to give an expressive answer to a generic question.
If you have more specific problems in the middle of the process you would probably be asking good questions. I hope others can give you some more relevant information other than meaningless suggestions.