Elves are strictly FORBIDDEN to remarry. Being immortal, their spouse exists until the end of Arda, so when you choose someone, you do so not only 'for life' but 'until the end of time.'
What Finwë starts out doing is pestering Mandos about when his wife is going to come back. When Míriel says 'never', Finwë is basically....wait a minute, I thought.....
And the Valar have a big debate in which they try to figure out what to do [we will not be showing this in our series] and a very 'legal' decision is reached, where, if Míriel promises to never be embodied again [EVER], then Finwë would be free to choose another wife. The statute of Finwë and Míriel issued by the Valar after lengthy debate and [I think] a year long waiting period allows the exception based on Míriel's promise.
It is heavily implied that Míriel later regrets her promise - that while she had zero desire to be re-embodied at the time, as time goes on and her spirit is healed, she feels differently about things. So, the 'if Finwë had been content....' line implies firstly that if he had just waited [a really, really long time], then eventually he and Míriel would have been reunited. Maybe.
When Finwë petitioned the Valar for permission to remarry, one of the reasons given (beyond, 'I miss my wife') was that he desired to have more children. Finwë and Indis have 2-5 children together (depending on which version of the story), and I would like to show them with 2 sons and 2 daughters. The 'not content' here definitely means that one son [Fëanor] wasn't enough for Finwë, and so Fëanor grows up as an only child of a dead mother whose father wants more children.
The relationship of Finwë and Indis is portrayed as love - he sees her in Valmar, with the light of the Trees in her hair, and is struck by her beauty. She had (apparently) always loved him, but he was already taken so she had just remained single since she couldn't have who she wanted. [Or something] I would not want to portray this as a marriage of convenience, or a 'political wedding' to unite the Noldor and the Vanyar. This is meant to be an opportunity for happiness, and the sour note (that turns to disaster) is not entirely Finwë's fault. In the end, Indis is left in Tirion when Finwë goes with the banished Fëanor to Formenos, and she lives as a widow in Valinor after the Darkening (while Finwë and Míriel are perhaps reunited in the Halls of Mandos).
I think the idea of a young Fëanor visiting the 'sleeping' body of his mother as a child is a good one. His father bringing him for these 'graveside visits' could be a good opportunity to show them both mourning. They can both talk to her as if she were there, giving updates on the family, and saying how they miss her, and Finwë can weep over her (maybe not with young Fëanor present). The beauty of the location contrasted with the grief should be quite poignant. (Everyone expects funerals to happen on rainy days, but of course in real life the weather does not match the mood.)
It would be possible to paint Indis as an evil stepmother, trying to erase the memory of Míriel and having a haughty 'Real Housewives' persona. But I would rather not. Indis and Fëanor will fail spectacularly to get along, and the failing should be on both sides, but....let's not make her a witch.