Obviously I know that doing magic in front of Muggles is against the wizard laws.

But let’s say you have a wizard who is married to a Muggle.

The Muggle is aware that magic exists due to having a Muggle-Born wizard in their family.

Is the wizard allowed to use magic?

Yes, it seems like it would be allowed.

Muggles who marry wizards are allowed to know about the wizarding world. Seamus’s mother told his father after they married.

“I’m half and half,’ said Seamus. ‘Me dad’s a Muggle. Mam didn’t tell him she was a witch ’til after they were married. Bit of a nasty shock for him.”
_{^{- Harry Potter and the Philosopher's Stone, Chapter 7 (The Sorting Hat)}}

Muggles who are allowed to know about magic seem to be allowed to see it being used and interact with magical items, as Justin Finch-Fletchley had his Muggle mother read Lockhart’s books.

“My name was down for Eton, you know, I can’t tell you how glad I am I came here instead. Of course, mother was slightly disappointed, but since I made her read Lockhart’s books I think she’s begun to see how useful it’ll be to have a fully trained wizard in the family …”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 6 (Gilderoy Lockhart)}}

Lockhart’s books are obviously magical, since the pictures of him on their covers move, and the content would be about magic.

“Written across it in fancy gold letters were the words: Gilderoy Lockhart’s Guide to Household Pests. There was a big photograph on the front of a very good-looking wizard with wavy blond hair and bright blue eyes. As always in the wizarding world, the photograph was moving; the wizard, who Harry supposed was Gilderoy Lockhart, kept winking cheekily up at them all.”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 3 (The Burrow)}}

The Grangers, both Muggles, were allowed into Flourish and Blotts, a wizarding bookstore where it’s likely they would witness magic.

“They each grabbed a copy of Break with a Banshee, and sneaked up the line to where the rest of the Weasleys were standing with Mr and Mrs Granger.”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 4 (At Flourish and Blotts)}}

Since they’re allowed into places exclusively for wizards, where others would be using magic, it’s almost certain that Muggle spouses of wizards are allowed to see their spouse or child use magic. The Dursleys witness people using magic several times, including wizards who’d know the laws, like Mr. Weasley.

“Fred scrambled around, cramming them back into his pocket, then gave the Dursleys a cheery wave, stepped forward and walked right into the fire, saying, ‘The Burrow!’ Aunt Petunia gave a little shuddering gasp. There was a whooshing sound, and Fred vanished.

‘Right then, George,’ said Mr Weasley, ‘you and the trunk.’

Harry helped George carry the trunk forward into the flames, and turn it onto its end so that he could hold it better. Then, with a second whoosh, George had cried, ‘The Burrow!’ and vanished too.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 4 (Back to the Burrow)}}

Dumbledore also uses magic in front of the Dursleys.

“Vernon Dursley had entered the room, Petunia at his shoulder and Dudley skulking behind them both.

‘Yes,’ said Dumbledore simply, ‘I shall.’ He drew his wand so rapidly that Harry barely saw it; with a casual flick, the sofa zoomed forwards and knocked the knees out from under all three of the Dursleys so that they collapsed upon it in a heap. Another flick of the wand and the sofa zoomed back to its original position.”
_{^{- Harry Potter and the Half-Blood Prince, Chapter 3 (Will and Won’t)}}

Though he’s doing it to amuse himself, it’s unlikely he’d do it if it was actually made illegal by the Ministry.

“Harry looked round; all three of the Dursleys were cowering with their arms over their heads as their glasses bounced up and down on their skulls, the contents flying everywhere.

‘Oh, I’m so sorry,’ said Dumbledore politely, and he raised his wand again. All three glasses vanished. ‘But it would have been better manners to drink it, you know.”
_{^{- Harry Potter and the Half-Blood Prince, Chapter 3 (Will and Won’t)}}

Presumably, since they were all allowed to do magic in front of the Dursleys, there doesn’t seem to be any restrictions on doing magic in front of Muggles who are allowed to know about it.

Most likely it is allowed.

If we think about it, the danger of using magic in front of muggles is due to the risk of exposing the wizard community. As long as the muggle is already aware of the magic, their partner's and kid's abilities, I think it is safe to assume that such wizards are allowed to do magic in front of their significant ones (or other not magical members of the family).

For example, Lily's family (and later Petunia's family) were muggles and Lily openly did magic in front of them. Dursley family also knew of Harry's origins and the only wrong when he did magic seemed to be reasoned by him being forbidden to do magic outside of Hogwarts as an underage wizard.

Harry Potter and the Chamber of Secrets:

Dear Mr. Potter,
We have received intelligence that a Hover Charm was used at your
place of residence this evening at twelve minutes past nine.
As you know, underage wizards are not permitted to perform spells outside school, and further spellwork on your part may lead to expulsion from said school (Decree for the Reasonable Restriction of Underage Sorcery, 1875, Paragraph C).