Hi J.,
I'm a home child care provider myself and a mother myself. So I have 2 points of view on this one from a providers perspective and one from a mothers perspective.
So 1st if your baby is being breastfed and formula fed at the sametime then there will be a little bit of a difference as far as time frame and the amount they eat. Breast milk is not as filling as formula so that could be your difference there.
Also not matter whether he is at home with you or at daycare he should be fed between every 3 and 4 hours but no more than 5 hours with out a feeding.
My youngest 2 kids were big eaters. My 3rd child was eating 8 ounce bottles every 3 hours by 2 1/2 months and weighed 16 pounds, we put her on cereal. The 4th was eating 8 ounce bottles every 4 hours when she was 3 1/2 months old so we started her on cereal also. My point in telling you this is I don't think he is being overfed, but I do think he may be hungrier at one time more than the other and he might be on the path to taking more.
Another part to this, no matter where you take your baby to be cared for you and the provider or center need to have "effective and open communication" with each other. And you need to give them an outline to go with. So from my perspective and what I do with my daycare kids and will start here soon because I will be watching a new baby is this.
Lets say he wakes up 6:00 am and he is on a every 3 hour feeding schedule, heres how it should look:
6:00 am bottle, diaper change and ready for daycare
9:00 am diaper, bottle, play for a bit and back down for a nap
12:00 (noon) diaper, bottle, paly for a bit and down for another nap
3:00 pm diaper, bottle, play and then depending on what time you would be ther to pick him up he should either A) be awake, B) playing, C) laying down, or D) just got up from a nap.
So your night time routine should look something like this:
Between 3 pm and 6 pm you pick him up.
6:00 PM you do the same diaper, bottle play for a bit.
8:00 pm Bath time
9:00 pm Bottle and bed time.
With him being on an every 3 hour feeding schedule no matter if you give him formula or breastmilk he should eat at the sametime if you give him the same amount. You have a couple of different options and for a little it may be trial and error, but you do have a few options, such as:
Let your provider(s) know that you want them to A) always use all of the breastmilk first because that is what you would prefer him to have (he make take 6 ounces of BM) and then finish the rest of the feedings with formula (which he only may need 4 ounces of formula to be full.
B) use 4 ounces of BM and 2 ounces of formula for each feeding to make 6 ounces total. Until all breastmilk is gone even if there is only an ounce left.
C) with the outline I gave you that means they would feed him 3 times while he is there so they could put 2 ounces of breastmilk in each one and add 4 ounces of formula.
Or D) the final option and label it:
on the outside of the bottle put 9 am bottle, 12 noon bottle, and 3 pm bottle. In each one of these bottles put what you want in them- one of the scenerios above. ALL 3 of these bottles should be empty when you return back to get him in the evening. You already send the breastmilk and have to keep his bottles cold it would be no different than making him a formula bottle.
And for good measure in case you have to stop where before going home put one extra bottle in there with 6 ounces of formula, you can get one of those things that you can just put the formula you need in there, a bottle of water and the bottle, that way there is always an extra. By what I gave you he should at least take around 4 - 6 ounces at each feeding, so over the 24 hour period with 3 at daycare and 3 with you he should take in 24 - 36 ounces, which he would be right on target for.
Anyway hope this helps and you get it worked out, W.