Advice for having my puppy around parents’ reactive senior dog

I got a 4 month old less than a week ago we’re only just starting her training. My family have a reactive 13 year old (who is big enough to do damage). She’s an angel with people but very poorly socialized with new dogs and got in occasional bad fights back when they had two dogs. My parents are struggling with the idea that I might skip Thanksgiving (and down the line Christmas.) We tried to introduce the two of them on a walk today so that neither was on their home turf, but their dog was barking, both were pulling, and then theirs lunged when they got close causing my puppy to start growling at her. We immediately went our separate ways.

I am more than happy to skip holidays to prioritize my puppy’s safety and cause our old girl as little anxiety as possible, but figured I’d exhaust all options first to try and make my family happy (plus it would be lovely if eventually they could coexist — it’s hard for me to accept I’ll miss old girl’s last years.) If we try to introduce them again I expect I’ll hire a trainer to be there, but in the meantime does anybody have experience with and/or tips on how to introduce a reactive senior to a puppy to at least the point that they can be separated in the same house without going insane? Am I best off just accepting that until my puppy can handle being alone I can’t be at my family’s home?