You should only consider switching when your current software has a significant flaw or lacks features that force you to spend excessive time on workarounds.

So, I would presume that if a tenant sent a partial electronic payment I could simply refund it even at the court hearing claiming that I am not accepting the payment.

Their lack of excuse really doesn't change anything because this isn't or at least should be personal to you. 

I have bought multiple properties personally, where rents were very low to begin with, and were even locked in for over a year, but once that renewal came up, I was able to simply raise the rent and keep the current tenant.

The time commitment the HH properties took from our company made them simply untenable to continue to manage. 

Does the tenant pay for the utilities as of now and you are simply upgrading the system? 

It was done simply because I enjoy helping in my very limited way. 

I would recommend them to get you set up for seeing all future bookings, the listing info and data, etc. and have them deal with it or simply ask them to switch their STR software to another platform specifically for those units under management...

And do your best not to let the lack of resources dictate your focus or goals.

And, ultimately, she is raising the money, which means that enough people trust the prospects of her performance.You simply have to decide where you stand and play or pass.