it is a good possibility. That is why I am looking for another location to put them.
I Had a major rat problem around my house. I used to keep my doors wide open at night in the summer time to cool down the house. I had rats invading my house going after the dog food and stashing it under the couch. The dog caught a couple of them but there were so many. about a month after we got our first ferret we never saw a single mouse or other rodent in or around our house. We even stopped having gopher mounds in our yard.
Only thing we could think of is we were tossing the litter in our flower gardens and hedges and that was keeping them away. That was 7 years ago still have not seen a single rodent. (besides the ones in the cages)
As for the mom eating the pinkies, I have no doubt it is because you moved her. You should always leave her in the cage. Mice are colony breeders and it is actually typically Good to have mom in the cage with other mice. The other females will help parent. As long as you have kept the male with the females (no removing him), and not allowed any other males in, you can keep the male in the cage as well. They only eat the young if there is stress or they have doubts as to the parentage. The males will often even help to parent their own young. The real problem with leaving the male in is that they will breed back to back, which is hard on the females. I have done both back to back breeding and moving daddy mouse into a separate cage. The big thing is to not move the female and babies. What I found worked best was to have a few breeding groups per male, and I would rotate the male through the groups of females, removing him when the females were close to birthing and putting him in with the next breeding group. This way I had a rotating supply of mice, and the females all got breaks between litters. I had a small bachelor pad cage for the male as well if I needed to wait longer before moving him into the next female cage. I really prefer to not breed back to back, it's too much strain on the momma mice.
Also, not sure what yor set up is like but I never allow wheels in the cage with breeding groups. I find that f can distract them from breeding, and when the babies come it can distract mom from caring for the babies. I have seen little pinkies get their faces ripped off by a spinning wheel trying to reach mom to nurse when mom was too busy running the wheel to care for the pups. It was really sad, and that mouse was not bred again, but it does happen that mice become addicted to the wheel for whatever reason and ignore their litter. I avoid they altogether by keeping wheels out of the cages. Once the babies are grttig closer to weaning age or between litters I will put the wheel back in. The bachelor pad and feeder cages where the litters aged to eating size got wheels, but not my active breeding cages.
so how long before I can clean the mouse cage after birth. I have been cleaning the cage weekly and the birth happened day before cleaning day. I did not want the pinkies in a filth cage that is why I moved them to a clean cage.
I like to give it a few days at least. You can just remove the dirtiest bedding from the areas of the cage that are Not the nest, and sprinkle in a little new bedding. I have never had a female flip out over that. If she did I wouldn't breed her again. You want to try to get good breeders that are nice and solid, good moms, handle stress well, produce fat healthy pups, etc.