Hello & welcome, I am Dr. B, a licensed veterinarian and I would like to help you with your wee ones today.
First, there is nothing wrong with having two puppies that are not related. To be fair, it can be a better option since we do sometimes see sibling puppies get along with one another but fail to develop social skills to interact with other dogs. Furthermore, if they have any genetic health issues (ie allergies, etc), then you would avoid the risk of both dogs being affected.
In regards ***** ***** playing and interaction, if they sleep together peacefully then this tells us that they are not adverse to one another. Instead, it sounds like they just need a little bit of training and rule establishment on your part.
First, if they do fight (not play-fight-- which can involve chewing/bite play), growl, or bully one another, then we have to intervene as soon as it happens. Whatever they are arguing over (ie toys, chews, etc), needs to be removed from the environment for the time being (in a few weeks when they have a better relationship, these may be returned). Our aim is to avoid any perceived rivalry between the two. Further to this, we need to make sure they each have their own food/water dishes, beds, and toys. This will reduce any feelings of competition between the two pups. Again if they are fighting over items like toys, they can have theirs only when separate from one another (ie in their own room or dog kennel).
If we see competition leading to fighting behavior with these pups, we do want to consider feeding them separately from one another at this stage. After meals, the food bowls should be picked up to ensure that this doesn't set off any challenges or arguments between them.
Furthermore, we do want them to interact but the level of doing so depends on how much play vs. fighting you are seeing. If they were completely adverse to one another, we'd have to consider introductions while they are on leashes (so they could be pulled apart). But from the sounds of it, your pups just sound like they may be playing initially but perhaps are getting overstimulated (leading to them playing too hard or that one may pushing the other too far in play leading to fighting). Therefore, we'd want to allow supervised play times. You will want to reward them (with positive praise and treats) when they are playing nice. If they get too rough, then you will want to intervene, say "no", and put them in "time out" from one another. After they have had time to settle (~5-10 minutes), you can allow them to be together again. If the negative behavior restarts, then back to time out for longer until they can settle down and interact properly with one another. The aim is to teach them what is ok, and what is not allowed.
Further to all of this, if they are being too rough with one another and cannot be trusted to behave when on their own, then you will need to consider separating them with you are not present to monitor them. Hopefully, this will not be necessary but we do need to do this if they are interacting negatively with one another because we don't want them fighting and undermining your training when you are not present to intervene.
Finally, do make sure to spend time with each puppy on its own. We want to make sure they feel that they are getting your attention as well. You can use these times for training or even having playtime with other dogs you may know (as long as they are all vaccinated already).
Overall, there is nothing wrong with having 2 puppies from different parents. The only issue is that you have 2 babies that need to learn how to interact with each other properly. Therefore, I would advise the above steps here. This will reduce competition and help you to make sure that their interactions with one another are positive ones. With time, they will learn that the negative behaviors are not acceptable and you will help them develop a positive relationship with one another. Finally, if you find that you are struggling, then consider asking your vet to refer you to your local behaviorist to help you further address this situation and teach these lads what you expect from them.
I hope this information is helpful.
If you need any additional information, do not hesitate to ask!
All the best,
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