Hi
Were you losing power in (receiving) City2 while playing it, or were you seeing this from the (supplying) City1 regional view?
When you purchase power from another city, it can take a bit for the game to synchronize the power usage. The regional view from the supplying City1 will sometimes show a "needs power" message for the receiving City2 even if you're selling it. If, when you go into City2, it is receiving power then it is all good. The cities don't advance in time while you're not playing them, so it's more than likely a synchronization thing. If both cities are running fine when you go in to manage them, then just proceed from there. You will not have the city go abandoned due to lack of power if you're not playing it.
That being said, regional synchronization can be confusing sometimes. If City1 is a couple of years ahead of the others, and sometime in the past had a glitch with the power (say, traffic got bad and the power plant didn't have any workers for a small time) you may forget about that and then later, while running City2, it suddenly loses power for no apparent reason - it could be catching up in time to that one glitch. At this point, you have plenty of power for the needs on your other city, just be aware that with any service sharing you want to be mindful of how much the other cities will need further down the line.
About the solar farm: Solar energy only replenishes during the daylight hours (6 am to 6 pm). Overnight, it is running on battery power, which only replenishes if you have surplus during the day. You may show that you have 200 mw surplus at noon, but that is probably not enough to run your entire city overnight. This is why you're losing power intermittently.
For both cases, you need to monitor the supply and usage over the course of a few days, and try to balance your building with the power availability. I would suggest monitoring how much available power you have in the first city for a few in-game days, see if there's a time of day where it drops significantly. Once you know you have a significant amount of power available, go into City2, turn off the solar farm and buy the power from City1 again. Then monitor and see how much power it draws. You need to give it some time to catch up to the first city. If you keep the solar farm on, make sure the setting to share power is turned off. That way, it will only draw power from City1 when it needs it. Be aware it will not be immediate - it does take a bit for the yellow power to flow from one city to another.
I hope this helps. If you're still having issues, please share some screenshots of your power data maps. I may be able to give you more specifics.
Happy Building!