Okay well you're dealing with some absolutes that can't be changed (and of course that's not meant to be any kind of a revelation! Just things to work around). Size, weight, energy level, age, immature social skills. It's a little misleading to assign our own "human" characteristics to the situation. Hoping that one dog will "understand" or the puppy will "forgive." This is about inter-canine relationship and honoring instinct. Of course either dog (regardless of physical size) can become the dominant dog (every relationship is dominant versus submissive, no matter how subtle the cues). You just don't want that play to escalate into a situation where one dog gets (accidentally) hurt and then over-reacts which can set up a chain reaction/retaliation, and then tips the balance. Is there a way where you can objectify the play time? Like teaching ball playing (with two balls please) so each one will run after one. (You might have to teach the game individually at first). Is there any way to tire out the puppy separately, or the Beagle if that's needed. Maybe a walk or game of tug with you in a different room/area. So that you're occasionally redirecting their energy/attention, not only just being focused on each other, but encouraging them to interact with you. I would create FUN time out zones for each one, x-pens or very comfortable crates. Teaching them that separate time is also a good thing. Maybe if they enjoy chewing on a Kong filled with something or some other busy activity. If they haven't been learning (what I call good citizenship) manners, they should be. The basics, your direction to "sit, down, stay, come." Please check out marker training (very fun, very rewarding). Again, you want to teach these dogs their focus should be on YOU not on one another. Although I figure the 2nd dog was introduced perhaps as a diversion, if you're a super busy person. Eventually as the puppy ages, they'll balance themselves, and communicate whether or not playtime works for both, but if not, each one should have their own safe space to chill out. (Remember, crates can have the doors left open, or no doors. As long they're not being used for punishment, they're not "prisons" as everyone thinks. They satisfy the dog's natural behavior for being in a "den.").