Wonky Gmail

Looking for those more techie savvy than I.

So anyone out there have trouble with Gmail.  I sporadically get "locked out."  It absolutely is making me nutty.  The weird thing is I do "two step" verification.  I also get this particular account on my phone.  It keeps telling me "try back in one hour or it can take up to 24 hours"  I have intermittently been able to get into it but then it goes wonky again.  What gives?

The weird thing is I am receiving emails on my phone.  I also can sign into my 3 other Gmail lesser used accounts.

And the even stranger thing is when I log into my husband's Gmail, it shows me online.  Now, I may very well have left myself signed in at home, but wouldn't it go "offline" after so many hours?

I thought the whole point of a Gmail type account was to be able to have multiple sign ins.