No don't feel weird about it... I think a lot of women/Moms can fleetingly feel this way, amidst their "Mother-In-Laws" presence... and their umbrella of a presence over their own child/baby.
Even Men can feel this way... for example: when we had our first child, my Hubby felt the same as you. And his feelings were founded, because my Mom "can" be a real overbearing/attached Grandma, even if she does not mean to. So, we've had to have discussions with her about it... because she was even "over-riding" my Hubby's and my "parenting" over our own child, ie: HER first Grandchild.
But, no matter what, YOU are your child's Mom. YOU need to make yourself present....visually and emotionally for your child, IN FRONT OF your MIL. Instead of being a "shrinking violet" around your baby, while in front of her. DO NOT be "insecure" about it... or your parenting style while she is around. Have a calm-quiet-gracious-confidence about it....
MOST Grandmas... will have the common sense NOT to "take over" the baby, when they are around... out of pure respect for YOU, the Mom. There DOES need to be boundaries however, if your MIL is the type that likes to take "control" over everything or is a "meddler."
SO... talk about it fully WITH YOUR HUSBAND. You BOTH have to be a "team" about it... and a united front about it, while the In-Laws are staying with you. Sure, it's nice they will then be able to babysit for you.... but, still, YOU are the parent. And like you are with your Nanny... you will NEED to brief your MIL about all the "do's" and "dont's" and 'rules" and your preferences when it comes to your child. Right? Do not just leave it up to your MIL/Grandma. SHE will have to "learn" about the ways and the rules about your child... and your/Hubby's way of living style.
Now, if it were me... I would keep your Nanny on... at least part time. If you do not... and then after your In-Laws leave... your Nanny might not be available for you anymore & you may lose her. She may by then have another job, or otherwise... as you know, the job market now is VERY competitive. So head's up if you want to KEEP your Nanny. Its not always easy to find another one. Don't take a Nanny for granted.
AND... your Nanny can be your MAIN go-to person, for your child or in informing you of anything... that you might not otherwise know. So even if the In-Laws will be around... it would be handy to have your Nanny... THEN YOUR SON WILL STILL HAVE HIS ROUTINE. Which to me is important. ALSO, AFTER the In-Laws leave... then that way you will have less of a headache to "transition" your son BACK into his routine, again. The more consistent you can keep it, the best. In the long run, for your son.. .and if you still have your Nanny around, then your son will not have to "miss her" or have to get used to having a Nanny all over again.
To me, having your sons life changed around or his schedule changed ONLY when the in-laws are here... then changed back to a Nanny again, might not be easy for him. And he will miss his Grandma too. So lots for your son to deal with too. That's why- keep it consistent, for him. AND keep his nap times and bedtimes the SAME, even when the in-laws are there. Or, you will regret it later, and your son's whole routine/schedule will need to be re-done after the undoing. Which is not always easy.
*Next, I would make sure that your In-Laws don't mind "babysitting" all day & everyday. Have you asked them first? I mean they will be staying with you for a long time. Maybe they want to relax too. So, I would make sure, you KNOW what their plans are. Babysitting a toddler all day & everyday, for some senior-citizens, can be tiring. And, you want to make sure they are able bodied and healthy and "able" to watch an active toddler. And are safe and know safety precautions.
To me... it's not your child/you that has to "give up" anything or any routines, just because the in-laws are coming over... because any gracious "guest" will realize that everyone has their lifestyle responsibilities to STILL keep up, whether or not they are visiting.
And, before the In-Laws come over... you have a nice discussion with your son about it. For example: because my Mom was so overbearing (she's much better now)... and controlling over my daughter.... we explained to our girl that Mommy & Daddy are her "parents"... WE decide things for her and we are the one's that give permission or not for things. We explained that even Grandma has to ask our permission first, for anything important. Thus, a child gains understanding of the whole parental "totem-pole."
Anyway, it should be fine. But what I"ve learned when you have extended-stay visitors in your home... you do NOT have to relinquish ANY of your Parental styles/values or daily routines... because the visitors are the ones who have to be flexible about it... they certainly can't expect a family to go AWOL on their own household or child's routines, especially when they are staying for so long. It's just common courtesy.
Al the best... your feelings are normal... don't worry. Just be present in your son's life as you always are now. You don't have to give up yourself or your son, just because the In-Laws/Grandma will be visiting your for a long time.
Take care,
Susan