I admire your wisdom in taking the time to research the move to a homeschooling lifestyle. I think that in doing this you are indeed following the promptings of the Holy Spirit. This is probably the single most important "leap" necessary when we are about to make a life choice that will affect those we love and our extended family as well.
Children the age of your daughter (11 years) are very fond of their peer group. You mention sleepovers, etc. and I gather from this comment alone that you are well aware of this importance. They enjoy talking, giggling and just being together. I think that if you are sensitive to this fact you will have no trouble in deliberately maintaining that close contact.
My daughters and sons have many friends that are not homeschooled and they have just as many that are. The issue at hand is how the children spend their time together. If the activities that your daughter is included in are always happening at the schools of her friends then this makes for a very lopsided relationship. It is important to make certain that you ask your daughter's friends to come to homeschool functions, family outings, and group activities that are an interest to your family. In so doing you are enjoying your lifestyle with your daughter's friends. This gives your daughter an opportunity to entertain and feel proud about the lifestyle of which she is now a part.
In the same respect, while you are researching the issues surrounding homeschooling look into the opportunities that are available in your area through homeschooling. See if there is a homeschool co-op to which you can belong. You may even be blest to have a Catholic homeschool group in your area that meets on a regular basis for fellowship and tutorial. Look into the local 4-H. Many times they have homeschool groups that meet once a month. This is a fine organization and has been very beneficial to my children. The lively competitions and activities are orientated to counties not to school groups. Therefore the children enjoy competing with neighboring counties as a team not as one school group against another. If you have access to it, community theater can be another excellent option to broaden a child's friendship base and meet on common ground.
Become active in your church as much as you are able and enjoy. Here is a place where the differences in lifestyle should not be a hindrance to friendship and fellowship.
Certainly there will be rough spots when you become fully committed to homeschooling and your lifestyle changes accordingly. I can tell you that you are already ahead of the game because you are sensitive to your family's needs and are trying very hard to move accordingly and in the will of the Holy Spirit. Face these concerns as they come up and allow for plenty of time for everyone to voice an opinion and work to resolve problem areas as a family with respect to the needs of your family's new lifestyle.
One of the moves that I have made that seemed too simple to work (but did) was to make a sure effort to keep my children on the schedule of the public school that their friends attend. We usually started later than these schools, but because we are homeschooling and can spend our time in a more concentrated way, we have been able to take fall break when they do and so forth. Now that most of my children are teens, this was important to them. They wanted to be out of school when their friends were out so they could do the sleepovers, etc.
I suppose the most important thing to remember when we are stepping into what we believe is the Father's will is the advice that Jesus gave us repeatedly, "Be not afraid." If the good and loving Lord is calling your family to a homeschooling lifestyle then He will surely give you the resources necessary to meet the goals.
I think that it is most important to keep praying and keep talking about issues as they arise. God bless your efforts.
I will be praying for you and your family. Again I admire your wisdom and your forthright nature. Surely you are a woman of prayer and this is your daughter's greatest asset. A mother who loves her and prays for guidance.
Dear Jesus, You gently guide us to the path that You would have us take. Loving Lord, keep us open and ready to respond to the promptings of Holy Spirit. In the world we are bound to face hardship, show us that peace that will surpass all hardship as we trust in Your gentle care of our lives. We love You, Lord Jesus. Amen.
Sending out a prayer,