regression with a new baby

Yes this is completely normal. Moms regress a little too (ask your husband!), and husbands regress too! When that new-baby energy is in the house, and that new-mom energy too, there is a strong pull to relive some of those earlier times and get some of that special connection. Childern can return to an earlier developmental state because they were very happy and well connected then, or because something wasn't right and they want a do-over. Either way, the playful parenting response is to go with it in a lighthearted manner. "Oh, my baby! Let me give you some special baby love!" Give extra cuddling and rocking time. Don't go overboard with "you're a big boy, you need to be grown up." Of course you will verbally reassure your older child that they are still precious to you, but don't expect the words to sink in. They have regressed! So words won't do the trick, you need to comfort them and assure them of yor love the way you do with a baby--your touch, the tone of your voice, the quality of your attention, your emotional bond.
If a particular regression behavior really really bugs you, you can try to deflect the regression to another area, but you can't get rid of that need (you might not even be able to deflect it, but you can try!) You can say, "I'm not crazy about that game, let's play a different baby game instead." (Make sure you don't say "baby" like an insult.