2 types of Logins - Working Remote Question

Alright, I hope this isn't to lengthy.
Currently I am working remote out of country with a VPN router and things have been good. I work 2 jobs atm, 1 uses an RSA token while the other uses a VPN tunnel to log in. - Both going through my VPN router that I get from STARvpn. This have been good for about a year.
Till recently.
2 other people who were also doing what I do in the company got caught. They were caught because IT turned on their WIFI on the computer remotely to see where they were. This has caused me to have bit of a panic. I am now back state side and looking for ways to leave both my work laptops at home.

I came across Tinypilot from a youtube and found it very interesting.
One of the common issues I see people having are meetings. For me that isn't a problem.
1 of my jobs I already have broken audio on my laptop, I have teams call me directly already for my mic and audio. That problem is an easy fix as they don't require any type of video.
The other job, uses google which I can connect via my phone for all my meetings. The one problem about that, is the times I have to share screen, but that can be resolved by logging into meeting twice which is fine.

So here is the question.

What kind of delays would I expect?
1 job already logs into a virtual deskstop and feels bit slow already. That is the RSR token one.
2 job I log into a server via VPN tunnel already, it does feel slow as currently I am using a 2 VPN setup (1 work 1 my router).

Do I still need my VPN router?
Say I buy 2 of these TinyPilots for both PCs. Do I still need my travel router to connect to them from out of country or doesn't matter as they are connected at home network for internet.

Any other comments or advice you have would be great. I would be interested in grabbing 2 of this really does work as intended.
Note I have 2 personal Laptops and 1 for each job to remote into.