I DM a 3.5 game and have a one year old. Yes, they will cause disruptions. They won't be the only things that do.
The truth about "immersion" is that disruptions happen. That's the reality of tabletop gaming. They happen because the kids are running around, or they wake up, or the phone rings, or you need to pull something out of the oven, or someone at the table tells a joke, or you don't know how to do a given thing in the rules and have to look it up...
If you actually managed to create a gaming space where immersion is not broken at least once during a session, you are doing something I've never been able to do in a tabletop game. (I have managed to do it at a LARP, but there's a lot more effort going into making that happen.)
My point? Set your expectations realistically. If you don't have a babysitter, there is no realistic chance of you going an entire session without the kids needing the attention of someone at the table.
If the one year olds are with a certain player, play at that person's home and play after bedtime. Mine tends to be asleep by 7:30, and usually sleeps long enough that we can usually get past 10:30 before he needs attention again.
If the kids do need attention and the person who needs to handle it is involved in what is currently happening in game, call a break. Go deal with it (because it won't get less distracting if you wait), and let everyone else go and get a drink and use the bathroom as needed. Once it's dealt with, resume the game.
If the person who needs to handle the given kid is not involved in what is currently happening game (party is split up or some other reason), that person can go handle it while the people who are involved keep playing.
It's also possible for the DM or a trusted player to take over another PC temporarily if someone has to go deal with real life, and that doesn't require stopping the game. I use this trick frequently in combat situations. Less so in social interaction ones, simply because it's harder for me to predict what a player will do when talking to the rest of the party (in combat, I know how my wife's Rogue is going to approach a situation and can take cues from the party leader).
Depending on how distracting the kids are, you might need to ask how to deal with them on Parenting SE instead.
Books & Other Immersion Breakers
One of the other problems you'll run into is that as a group of newbies, you don't know the rules. So in some cases you'll have to stop to look them up. If the DM does that and makes a ruling, don't spend a ton of time arguing about it. Nothing breaks immersion faster than rules arguments at the table.
Look at the rule, and make a ruling. If people don't agree and it can't be resolved quickly, go with what the DM says and sort it out between sessions. The middle of a combat encounter is not the place for a 30 minute discussion over what a spell does.