The last thing I would do to a dairy cow is to feed alfalfa pellets in place of hay when they are on pasture. A cow needs roughage, and the long stem kind is better than concentrate any day. I would keep some hay in front of her whether she is on pasture or not. All my family nurse cows have access to hay year round. They don't eat much if any during pasture/grazing season. They are grained daily as they usually have 2-4 calves on each of them, and I will separate the calves and milk once a day also, when I need the milk and to keep a good handle on the condition of their udders and the milk. But, after one DA on a young cow, I have found that a little hay is often the trick to help prevent it. I am sure most of my cows don't eat enough to make a difference, but it is there. If I feel that they need more protein, which the alfalfa pellets would provide, I just up the dairy pellets. We have a 38% concentrate dairy pellet available, usually for top dressing a silage bunk mix; that I will buy and mix a handful into their regular feed. 22% feed is a good amount of protein to feed with pasture and/or hay.
Since you don't sound like you are pushing her production I think just giving her the grain and good pasture and keeping a little hay available is fine. Lush spring grass is alot of water so they will be eating alot to satisfy their needs, and you also need to be careful of an imbalance in magnesium. Use a Hi-Mag mineral for her as her free choice mineral, so that she doesn't have a problem. They will get very loose on the lush green grass so don't be surprised if the manure gets pretty runny for a while as her gut adjusts. That is another reason to keep some hay available; to give it a little more consistency. If she drops condition, just give her a little more grain. Sometimes the jersey/holstein cross will make alot more milk and they will "milk the fat off their back" in the beginning. More grain will mean more milk, but they will be making a certain amount that they are genetically wired to do, and can lose condition easily. You don't want to push the production, but you want to make sure she is getting enough to keep up her condition. I have 1: 1/2- jer/hol, 1: 3/4jer-1/4 hol, 1: jer, 1: 1/2jer-1/2guernsey, 1 guernsey, 1: 1/2guernsey-1/2hol. The jer/hol and the guernsey/hol and the straight guernsey lose more weight when they are in production, than the others.
I think some of it is that the holsteins have just been bred for so much concentrate feeding over the years that they just don't do as well when they are not fed as much. For just a family cow that you are letting raise her calf also, I like a jersey/angus or a jersey/hereford cross. Not too much milk, and a little beefier and the calf will make a nice family beef if the cow was bred to a beef bull.