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It was 10 p.m. on Sunday when Gillian Parker and her husband Phillip got the call telling them that a mandatory evacuation order had been issued in the area of their New Territory, Texas, home due to the rising floodwaters of Hurricane Harvey.

The call took the Parkers by surprise given that forecasts had predicted waterfall would be 4-5 ft. below the southwest Houston neighborhood’s levees. But the couple, their 16-year-old daughter Allison Parker and her 81-year-old grandmother Sylvia Parker still packed what they could — splitting four adults and their three dogs between two cars and rushing for safety.

Zooming down the highway to try to get out of town, the Parkers hit a few roadblocks along the way — including a few dead ends and closed streets. One of their cars flooded too. But around midnight, they arrived at the only open hotel they could find: the Holiday Inn Express and Suites in Katy, Texas.

That’s where the Parkers got the harsh news that their three dogs — Arrow (a shepherd lab mix), Wiggum (a chocolate lab-hound mix) and Buttercup (a yellow lab) — would not be allowed into the hotel to stay with them.

“It’s ridiculous and outrageous,” Gillian, 47, tells PEOPLE. “This is an 800-year flood. Three exits down the highway, the national guard is pulling people out of their houses. And our dogs can’t come in to safety?”

She says she tried to problem-solve with management, begging to bring the pets in. But local management refused to budge, citing the hotel’s no-pet policy.

And corporate contacts told Gillian that because the Katy location is a franchise, there’s nothing they can do to immediately override the rule.

They’re never alone, Gillian says. She and Phillips take turns to sit in the car with the dogs at all times, even overnight. Allison helps out too, joining the cycle with her parents to take the dogs for walks.

“It’s pouring rain,” Gillian explains. “You’re soaked to the bone just getting there, and walking them is even worse. The rain felt like needles in your face. And you end up shivering in the car. It’s just… I’m just chagrined, irritated, cold, wet, tired, and exhausted.”

Asked why she didn’t just insist on bringing the dogs in, Gillian chalks it up to being a family of “rule-followers.”

“My husband’s English,” she says. “You stand in line and you wait your turn. You don’t bust your way in and do what you want.”

They are also worried about consequences if they did. “We’re afraid we’ll get kicked out,” she confesses. “I don’t want to lose my place in the hotel. At this point we’re so tired. And I’m afraid to leave. We hope we’re safe.”

Meanwhile floodwaters continue to rise around the Parkers. Their neighborhood is expected to be inundated Tuesday, the water levels predicted to bypass the 58-ft. levees. Major freeways are blocked. Small roads are out. Not a restaurant or grocery store is open nearby. They’re close to running out of bottled water. And they’ve stopped turning the car on too, worried they’ll run out of gas.

The storm has brought destructive rain to Texas’ largest cities — including Houston, Austin and San Antonio — and Louisiana, resulting in five deaths and 12 injuries, according to the latest reports.

PEOPLE reached out to the Holiday Inn General Manager Jim Hernandez, who as of Tuesday afternoon said the hotel has “not wavered” their policy “at this time.”

“Our hotel is a not pet-friendly hotel,” he said. “We do offer our guests areas where they can take their pets to be kenneled. There’s locations here down the street that are able to take their pets if they like.”

Holiday Inn’s corporate representative has not immediately responded to PEOPLE’s request for comment.

Per Gillian, it appears the kennel Hernandez referred to is currently closed. If it opens (and it’s safe), she will consider dropping the dogs off there after the storm passes. “If we were about to jump in the car and run for our lives, I would be nervous about it,” she says.

In the meantime, Gillian is hoping something will give with hotel management — who have since told her they’ve made exceptions to guests with smaller dogs but wouldn’t be able to with dogs her size.

“I’m playing nice right now but there’s a point at which I won’t be.” she reveals. “I’m biding my time. I am confident that they’re going to do the right thing.”

Who is responsible for your pets during a catastrophe? The kennel, you, the shelter or hotel?

Do you have a right to get upset when a business who never allowed pets to begin with, still refuses to accommodate Roscoe?

I love dogs. I’ve had several. But in this situation if I was a business owner, I’m not certain I’d allow dogs in my hotel. Especially not dogs larger than 20 pounds. I’m not trying to be rude, but dogs require a lot of attention. And having a hotel room with three large dogs is not cool to me. As the owner of the pets I’d be pissed too. But you have to understand. Everyone doesn’t see your dog as a cute little house pet. They see them as animals, capable of causing damage. Capable of shitting all over the hotel carpets, sidewalks etc.

So who is WRONG?