Show (more than tell) your family how your aikido practice is positively improving your personality and activities around the home - be careful to illustrate how your aikido practice makes you more pleasant/fun to be around.
Aikido is in the words of Ueshiba the art of "loving protection" it's practice is also based upon and rooted in respect. I think the sincere practice of REI (formal etiquette) is as important if not more important outside the dojo as it is before, during and after practice. If you want your aikido training to benefit you the most, then be sure to see your practice as something that is for the benefit of your family. Your practice should first of all raise your level of respect and appreciation for your family, they are in many ways the best teachers and training partners you can have.
Try to think of your aikido practice as personally making you a better mom and wife at home and not simply be an excuse to get out of the house and to escape whatever may be uncomfortable, unsatisfying or lacking there.
For your spouse, as someone else pointed out, "reassure him that you love him and respect and support him in his endeavors and hobbies". If you really want his support, show him how aikido is improving your desire to frequently receive and harmonize with him. That will surely fix his opposition.
Don't forget that your kids are your kids, and you're the mom, until they are of age they must abide by your rules - insist upon their help around the house because it will teach them responsibility, and will better prepare them for adulthood, but don't neglect your own responsibilities either as you go off to practice several times a week. If you have to go to the dojo one less day a week or forego some seminars for your family, do it. Consistently show them they are more important, and they won't need to resent your aikido.
In the dojo we learn to relax, and we learn to calmly and attentively face challenges and deal with them in mutually beneficial ways. Take those lessons home and make them your own private seminar/practice - your home is your dojo and your family members are your absolute best training partners whether they are cooperative or not. If you're going to practice aikido don't do it half heartedly. Make a commitment to use your practice as a means to lovingly protect and nourish your family relationships and to build your home into strong castle, a refreshing retreat and a sacred shine. There is no competition in aikido - so don't let your aikido practice compete with or against your family, and your home, it's not worth it.
YOUR family is far more important than your dojo family!
You still have to lead by example. Your own chores and activities at home, whether cooking, cleaning, decorating, gardening, or whatever are all opportunities to practice aikido! Who would've thought that sweeping, dusting, laundry, ironing, rearranging furniture, tending to the kids, and the like could become joyful activities for practicing aikido? You can integrate whole-body movement from your center with everything you do, you can smile at every challenging chore & situation, drop your center, breath deeply and infuse your approach with a creative positive spirit. You can learn to do things more efficiently, more elegantly, and you can find ways to express your loving care, awareness & attention (zanshin) around the house, and often do much more, with less. You will find that you can actually train at home, and that you will probably learn more (internally) than your dojo mates will at class anyway. Aikido as Ueshiba envisioned it is not about "techniques" as much as it is a "WAY". The way that you make it your own and internalize the lessons learned on the mat, is by integrating the principles into your daily life.
These ideas are not so much my own, but were impressed upon me by one of my instructors.