Is this a sign of an undesirable or bad pet ?

Put them in a crate at night.

Or lock them in a room with an easy to clean floor. And no – I would not be happy about it.

Yep, it would be unacceptable to me but you must take charge and confine them to a pen or crate with pee and poop liners spread out.
They obviously don’t want to go out in the rain so you know that and need to figure out how to keep them confined at night to avoid house soiling.

My dog goes out right before bed time and doesn’t have to go again until we get up the next day. I’m wondering why your dogs can’t hold it for 7 or 8 hours. Could there be a medical reason?

Why are they pooping at night? Are you not taking them out in the evening and walking them until they poop?

No way would I put up with messes on the floor. I’d have kennels outside for dogs that did that.

If this is happening more than very rarely, you are not walking them enough. If you don’t want to walk them on leash, then at least play with them outdoors before dark, a lot of movement will promote the moving of their bowels outside. I would not go out in the rain either if Pooping inside was allowed.
Crate training, if they are not too old and averse to it is also a good idea. (Sometimes older dogs never take to it.)

Are these the same dogs?

Well…while the behaviour is a major concern, I don’t think the dogs can be held responsible for their housetraining.

Dogs need exercise, training and patience. Your particular dogs may benefit from a litter box.

Since your post that @canidmajor has provided the link for above, have you put any more work into training and exercising these dogs? If the answer is no then this isn’t a sign of a bad pet but a sure sign of a bad owner. If you have put in more work but you are struggling to get the results you want I would recommend getting in touch with a positive behaviourist to help you out with these dogs. Either way, it has been clear in a number of your questions about your dogs that you need help to give these dogs what they need which will hopefully enable you to get what you need from the dogs.

I know someone with small toy dogs, three of them in fact. He doesn’t walk them. he only let’s them out in a yard to sniff and play a few times a day. They make messes and wake him up every night. He keeps them inside. To me, it sounds like a nightmare. I would never live like that.

It is my husband’s fault. We crate them (and they go willingly) at 6pm each night. Then around 2–3 am my husband gets up to use the bathroom and lets them out so they can jump up on the bed or sofa. That’s when they go on the rugs. We have three baby gates up each night to keep them out of the rooms with the rugs so they wait until one is taken down during the day to go get the mail or answer the door. Brazenly, they sometimes choose the daytime to go on a rug as soon as one of those baby gates comes down. If he neglects to unlock the gate due to being exhausted , one of them begins barking to be let out in the middle of the night.
He created a monster but , amazingly, he doesn’t care! He has never uttered a word about the stained, smelly rugs!

You crate them at six p.m.? If they are not let out, do they have to hold it until morning? When do you get up?

At this point I can’t see how it matters whose fault it is. They will continue this behavior as long as it is allowed. If these are the same dogs they’ve had four more years to cement this behavior, as have you. Since you won’t bother to do anything to change this, you might want to reconsider keeping these dogs. If they are “undesirable” or “bad” you and your husband have made them so.

Bichons are usually excellent pets, bright and fairly easy to house train. They may be able to be re-homed, even at this age, to owners who are willing to take the time to care for them that they deserve.

You could put them in crates, but if they’re not used to being in a crate, they will howl, whine, bark and try to chew their way out of it, until they drive you nuts! lol.

Put the dogs outside with doggie houses. You may need to chain them by their dog house, otherwise they will be scratching your door down at night! But they will be fine.
Your vet can prescribe them tranquilizers if they bark constantly and disturb your neighbors.

Get them used to living outside, spend time outside with them, read a book outside while they play. Give them the idea that outside is safe and has comforts also. Give them chew toys, but most importantly, get the dogs used to relieving themselves outside in the grass.

Your rugs texture may appear as grass to them.
Keep chew bones and treats on your rugs to stop them from wanting to relieve them self where they are eating and snacking.

Allow them inside for short visits only when you’re home with them. You can have a dozen short visits in one day ranging from 15 minutes to 45 minute visits. But don’t let them in overnight yet, unless one of your dogs is not relieving itself in your house, then allow that “potty trained dog” inside at night. It’s usually the dominant dogs that tend to relieve themselves inside the home, even though they know they are wrong to do it.

Keeping them outside retrains them to know, rain or shine, their bathroom is outside.

When you allow them short ‘visits’ inside, they will be humbled to come inside. They’ll be reminded of all the comforts there is to being inside. Mostly, these visits shows them their acceptance into the “pack”, that you still love them and they thrive for your attention. Other comforts are the soft rugs, no rain, snacks, toys and they become more playful inside.

Use this reward of short inside visits to your advantage. Let them differentiate between the comforts inside and that their bathroom is outside.

You will need to train them to respect your home, and continue to remind them to go outside to use the bathroom; especially when it’s raining. If they fear the rain play or walk with them in the rain or garden sprinkler so they will get used to being wet. Make sure they have a warm bed to lay down inside if they come in wet. Old dogs get arthritis and hurt just like old people.

In time, they will appreciate your home and respect it when you gradually allow them back in as indoor dogs again.

^ I’m sure you mean well, but this… :

“Put the dogs outside with doggie houses. You may need to chain them by their dog house, otherwise they will be scratching your door down at night! But they will be fine. Your vet can prescribe them tranquilizers if they bark constantly and disturb your neighbors.”

…is called animal abuse. You can’t just toss indoor dogs outside because you haven’t bothered to train them.